4x(x-3)+12=-2x+36

Solution for 4x(x-3)+12=-2x+36 equation:

4x(x-3)+12=-2x+36

We move all terms to the left:

4x(x-3)+12-(-2x+36)=0

We multiply parentheses

4x^2-12x-(-2x+36)+12=0

We get rid of parentheses

4x^2-12x+2x-36+12=0

We add all the numbers together, and all the variables

4x^2-10x-24=0

a = 4; b = -10; c = -24;
Δ = b2-4ac
Δ = -102-4·4·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*4}=\frac{32}{8}
=4
$