4X² + 12x - 40 = 0 formula general con procedimiento : )?

4X² + 12X - 40 = 0 (Podemos simplificar por 4)

X² + 3X - 10 = 0

Por factorizacion :

X² + 3X - 10 = 0

3X = 5X - 2X

X² + 5X - 2X - 10 = X² - 2X + 5X - 10

(X² - 2X) + (5X - 10) = X(X - 2) + 5(X - 2)

X(X - 2) + 5(X - 2) = (X + 5)(X - 2)

X² + 3X - 10 = (X + 5)(X - 2)

Por formula general.

4X² + 12X - 40 = 0

Donde : a = 4 ; b = 12 ; c = - 40

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-%2812%29%5Cpm%20%5Csqrt%7B%2812%29%5E2-4%284%29%28-40%29%7D%7D%7B2%284%29%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-12%5Cpm%20%5Csqrt%7B144%20%2B640%7D%7D%7B8%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-12%5Cpm%20%5Csqrt%7B784%7D%7D%7B8%7D" />

<img src="https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-12%5Cpm%20%5C%2028%7D%7B8%7D" />

X1 = [ - 12 + 28] / 8 = 16 / 8 = 2

X1 = 2

X2 = [ - 12 - 28] / 8 = - 40 / 8 = - 5

X2 = - 5

Soluciones : X = 2 y X = - 5

4X² + 12X - 40 = (X - 2)(X + 5).