4x(x-2)=-8x+36

Solution for 4x(x-2)=-8x+36 equation:

4x(x-2)=-8x+36

We move all terms to the left:

4x(x-2)-(-8x+36)=0

We multiply parentheses

4x^2-8x-(-8x+36)=0

We get rid of parentheses

4x^2-8x+8x-36=0

We add all the numbers together, and all the variables

4x^2-36=0

a = 4; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·4·(-36)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*4}=\frac{24}{8}
=3
$