(12-2x)(15-2x)=135

Solution for (12-2x)(15-2x)=135 equation:

(12-2x)(15-2x)=135

We move all terms to the left:

(12-2x)(15-2x)-(135)=0

We add all the numbers together, and all the variables

(-2x+12)(-2x+15)-135=0

We multiply parentheses ..

(+4x^2-30x-24x+180)-135=0

We get rid of parentheses

4x^2-30x-24x+180-135=0

We add all the numbers together, and all the variables

4x^2-54x+45=0

a = 4; b = -54; c = +45;
Δ = b2-4ac
Δ = -542-4·4·45
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{61}}{2*4}=\frac{54-6\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{61}}{2*4}=\frac{54+6\sqrt{61}}{8}
$