(15-2x)(12-2x)=300/2

Solution for (15-2x)(12-2x)=300/2 equation:

(15-2x)(12-2x)=300/2

We move all terms to the left:

(15-2x)(12-2x)-(300/2)=0

We add all the numbers together, and all the variables

(-2x+15)(-2x+12)-150=0

We multiply parentheses ..

(+4x^2-24x-30x+180)-150=0

We get rid of parentheses

4x^2-24x-30x+180-150=0

We add all the numbers together, and all the variables

4x^2-54x+30=0

a = 4; b = -54; c = +30;
Δ = b2-4ac
Δ = -542-4·4·30
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{609}}{2*4}=\frac{54-2\sqrt{609}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{609}}{2*4}=\frac{54+2\sqrt{609}}{8}
$