(240+x)(375+x)=180000

Solution for (240+x)(375+x)=180000 equation:

(240+x)(375+x)=180000

We move all terms to the left:

(240+x)(375+x)-(180000)=0

We add all the numbers together, and all the variables

(x+240)(x+375)-180000=0

We multiply parentheses ..

(+x^2+375x+240x+90000)-180000=0

We get rid of parentheses

x^2+375x+240x+90000-180000=0

We add all the numbers together, and all the variables

x^2+615x-90000=0

a = 1; b = 615; c = -90000;
Δ = b2-4ac
Δ = 6152-4·1·(-90000)
Δ = 738225
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:

$\sqrt{\Delta}=\sqrt{738225}=\sqrt{225*3281}=\sqrt{225}*\sqrt{3281}=15\sqrt{3281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(615)-15\sqrt{3281}}{2*1}=\frac{-615-15\sqrt{3281}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(615)+15\sqrt{3281}}{2*1}=\frac{-615+15\sqrt{3281}}{2}
$