Alguien que me ayude a resolverlo con la fórmula general por favor , con procedimiento para que pueda entender dónde me equivoqué ?

<img src="https://tex.z-dn.net/?f=%282x%2Bc%29%5E2%3D2x-c%20%5C%5C%5B2pt%5D%0A%5Ctext%7BEn%20el%20lado%20izquierdo%20se%20usa%20%7D%20%5C%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%20%5C%5C%5B2pt%5D%0A%282x%29%5E2%2B2%282x%29%28c%29%2Bc%5E2%3D2x-c%20%5C%5C%5B2pt%5D%0A4x%5E2%2B4xc%2Bc%5E2%3D2x-c%20%5C%5C%5B2pt%5D%0A%5Ctext%7BAhora%20se%20pasa%20todo%20a%20un%20lado%20y%20se%20suman%20los%20t%5C%27erminos%20semejantes%7D%5C%5C%0A%5Ctext%7Bconsiderando%20que%20la%20variable%20es%20%7D%20x%20%5C%5C%5B2pt%5D%0A4x%5E2%2B%284xc-2x%29%2B%28c%5E2%2Bc%29%3D0%20%5C%5C%5B2pt%5D%0A4x%5E2%2B%284c-2%29x%2Bc%5E2%2Bc%3D0%20" />

<img src="https://tex.z-dn.net/?f=%5Ctextbf%7BF%5C%27ormula%20general%20%3A%20%7D%5C%5C%5B2pt%5D%0Aax%5E2%2Bbx%2Bc%20%5C%20%5CRightarrow%20%5C%20x%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BPara%20usar%20la%20f%5C%27ormula%20reemplazamos%20%3A%7D%20%5C%5C%0Aa%3D4%20%5C%20%2C%20%5C%20b%3D4c-2%20%5C%20%2C%20%5C%20c%3Dc%5E2%2Bc%20%5C%5C%5B4pt%5D%0Ax%3D%5Cdfrac%7B-%284c-2%29%5Cpm%20%5Csqrt%7B%284c-2%29%5E2-4%284%29%28c%5E2%2Bc%29%7D%7D%7B2%284%29%7D%20%20%5C%5C%5B2pt%5D%0Ax%3D%5Cdfrac%7B-4c%2B2%5Cpm%20%5Csqrt%7B16c%5E2-16c%2B4-16c%5E2-16c%7D%7D%7B8%7D%20%20%5C%5C%5B2pt%5D%0Ax%3D%5Cdfrac%7B-4c%2B2%5Cpm%20%5Csqrt%7B4-32c%7D%7D%7B8%7D%3D%5Cdfrac%7B-4c%2B2%5Cpm%20%5Csqrt%7B4%281-8c%29%7D%7D%7B8%7D%20%20%5C%5C%5B2pt%5D%0Ax%3D%5Cdfrac%7B-4c%2B2%5Cpm%202%5Csqrt%7B1-8c%7D%7D%7B8%7D%3D%5Cdfrac%7B2%28-2c%2B1%5Cpm%20%5Csqrt%7B1-8c%7D%5C%2C%29%7D%7B8%7D%20%20%5C%5C%5B2pt%5D%0Ax%3D%5Cdfrac%7B-2c%2B1%5Cpm%20%5Csqrt%7B1-8c%7D%7D%7B4%7D%20%20" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BSeparando%20se%20obtienen%20las%202%20soluciones%20%3A%7D%20%20%5C%5C%5B4pt%5D%0Ax%3D%5Cdfrac%7B1-2c%2B%5Csqrt%7B1-8c%7D%7D%7B4%7D%20%5C%20%5C%20%5Cvee%20%5C%20%5C%20x%3D%5Cdfrac%7B1-2c-%5Csqrt%7B1-8c%7D%7D%7B4%7D" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BAll%5C%27i%20ya%20est%5C%27a%20la%20respuesta%20%2C%20pero%20dada%20la%20forma%20del%20ejercicio%20se%20puede%7D%5C%5C%0A%5Ctext%7Btrabajar%20de%20una%20forma%20m%5C%27as%20sencilla%20%2C%20veamos%20%3A%7D%20%5C%5C%5B2pt%5D%0A%282x%2Bc%29%5E2%3D2x-c%20%5C%5C%5B2pt%5D%0A%282x%2Bc%29%5E2%3D%282x%2Bc%29-2c%20%5C%5C%5B2pt%5D%0A%5Ctext%7Bse%20realiza%20un%20cambio%20de%20variable%20%2C%20%7Du%3D2x%2Bc%20%5Ctext%7B%20%2C%20%20reemplazando%7D%20%5C%5C%5B2pt%5D%0Au%5E2%3Du-2c%20%5C%20%5CRightarrow%20%5C%20u%5E2-u%2B2c%3D0%20%5C%5C%5B2pt%5D%0A%5Ctext%7BSe%20resuelve%20por%20f%5C%27ormula%20para%20la%20variable%20%7Du%20%5C%5C%5B4pt%5D%0Au%3D%5Cdfrac%7B-%28-1%29%5Cpm%20%5Csqrt%7B%28-1%29%5E2-4%281%29%282c%29%7D%7D%7B2%281%29%7D%3D%5Cdfrac%7B1%5Cpm%20%5Csqrt%7B1-8c%7D%7D%7B2%7D%0A" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BAhora%20se%20repone%20la%20variable%20original%20%2C%20sabiendo%20que%20%7D%20%5C%202x%2Bc%3Du%20%5C%5C%5B2pt%5D%0A2x%2Bc%3D%5Cdfrac%7B1%5Cpm%20%5Csqrt%7B1-8c%7D%7D%7B2%7D%20%5C%5C%5B2pt%5D%0A2x%3D%5Cdfrac%7B1%5Cpm%20%5Csqrt%7B1-8c%7D%7D%7B2%7D-c%3D%5Cdfrac%7B1-2c%5Cpm%20%5Csqrt%7B1-8c%7D%7D%7B2%7D%20%5C%5C%5B2pt%5D%20%5C%5C%5B2pt%5D%0Ax%3D%5Cdfrac%7B1-2c%5Cpm%20%5Csqrt%7B1-8c%7D%7D%7B4%7D%20%5C%5C%5B4pt%5D%0A%5Ctext%7BSe%20separan%20las%20soluciones%20%20%3A%7D%20%5C%5C%5B4pt%5D%0Ax%3D%5Cdfrac%7B1-2c%2B%5Csqrt%7B1-8c%7D%7D%7B4%7D%20%20%5C%20%5C%20%5Cvee%20%5C%20%5C%20x%3D%5Cdfrac%7B1-2c-%5Csqrt%7B1-8c%7D%7D%7B4%7D%20" />.