(240+x)(375+x)=101250

Solution for (240+x)(375+x)=101250 equation:

(240+x)(375+x)=101250

We move all terms to the left:

(240+x)(375+x)-(101250)=0

We add all the numbers together, and all the variables

(x+240)(x+375)-101250=0

We multiply parentheses ..

(+x^2+375x+240x+90000)-101250=0

We get rid of parentheses

x^2+375x+240x+90000-101250=0

We add all the numbers together, and all the variables

x^2+615x-11250=0

a = 1; b = 615; c = -11250;
Δ = b2-4ac
Δ = 6152-4·1·(-11250)
Δ = 423225
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:

$\sqrt{\Delta}=\sqrt{423225}=\sqrt{2025*209}=\sqrt{2025}*\sqrt{209}=45\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(615)-45\sqrt{209}}{2*1}=\frac{-615-45\sqrt{209}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(615)+45\sqrt{209}}{2*1}=\frac{-615+45\sqrt{209}}{2}
$