(4x-8)(x-12)=180

Solution for (4x-8)(x-12)=180 equation:

(4x-8)(x-12)=180

We move all terms to the left:

(4x-8)(x-12)-(180)=0

We multiply parentheses ..

(+4x^2-48x-8x+96)-180=0

We get rid of parentheses

4x^2-48x-8x+96-180=0

We add all the numbers together, and all the variables

4x^2-56x-84=0

a = 4; b = -56; c = -84;
Δ = b2-4ac
Δ = -562-4·4·(-84)
Δ = 4480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{70}}{2*4}=\frac{56-8\sqrt{70}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{70}}{2*4}=\frac{56+8\sqrt{70}}{8}
$