(12-2x)(5-2x)=180

Solution for (12-2x)(5-2x)=180 equation:

(12-2x)(5-2x)=180

We move all terms to the left:

(12-2x)(5-2x)-(180)=0

We add all the numbers together, and all the variables

(-2x+12)(-2x+5)-180=0

We multiply parentheses ..

(+4x^2-10x-24x+60)-180=0

We get rid of parentheses

4x^2-10x-24x+60-180=0

We add all the numbers together, and all the variables

4x^2-34x-120=0

a = 4; b = -34; c = -120;
Δ = b2-4ac
Δ = -342-4·4·(-120)
Δ = 3076
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:

$\sqrt{\Delta}=\sqrt{3076}=\sqrt{4*769}=\sqrt{4}*\sqrt{769}=2\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{769}}{2*4}=\frac{34-2\sqrt{769}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{769}}{2*4}=\frac{34+2\sqrt{769}}{8}
$