-4x(x-2)+3(x+7)=12

Solution for -4x(x-2)+3(x+7)=12 equation:

-4x(x-2)+3(x+7)=12

We move all terms to the left:

-4x(x-2)+3(x+7)-(12)=0

We multiply parentheses

-4x^2+8x+3x+21-12=0

We add all the numbers together, and all the variables

-4x^2+11x+9=0

a = -4; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-4)·9
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{265}}{2*-4}=\frac{-11-\sqrt{265}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{265}}{2*-4}=\frac{-11+\sqrt{265}}{-8}
$