(240+x)(375+x)=130500

Solution for (240+x)(375+x)=130500 equation:

(240+x)(375+x)=130500

We move all terms to the left:

(240+x)(375+x)-(130500)=0

We add all the numbers together, and all the variables

(x+240)(x+375)-130500=0

We multiply parentheses ..

(+x^2+375x+240x+90000)-130500=0

We get rid of parentheses

x^2+375x+240x+90000-130500=0

We add all the numbers together, and all the variables

x^2+615x-40500=0

a = 1; b = 615; c = -40500;
Δ = b2-4ac
Δ = 6152-4·1·(-40500)
Δ = 540225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{540225}=735$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(615)-735}{2*1}=\frac{-1350}{2}
=-675
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(615)+735}{2*1}=\frac{120}{2}
=60
$