(25-2x)(15-2x)-231=375

Solution for (25-2x)(15-2x)-231=375 equation:

(25-2x)(15-2x)-231=375

We move all terms to the left:

(25-2x)(15-2x)-231-(375)=0

We add all the numbers together, and all the variables

(-2x+25)(-2x+15)-231-375=0

We add all the numbers together, and all the variables

(-2x+25)(-2x+15)-606=0

We multiply parentheses ..

(+4x^2-30x-50x+375)-606=0

We get rid of parentheses

4x^2-30x-50x+375-606=0

We add all the numbers together, and all the variables

4x^2-80x-231=0

a = 4; b = -80; c = -231;
Δ = b2-4ac
Δ = -802-4·4·(-231)
Δ = 10096
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:

$\sqrt{\Delta}=\sqrt{10096}=\sqrt{16*631}=\sqrt{16}*\sqrt{631}=4\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{631}}{2*4}=\frac{80-4\sqrt{631}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{631}}{2*4}=\frac{80+4\sqrt{631}}{8}
$