(375+x)*(275+x)=130500

Solution for (375+x)*(275+x)=130500 equation:

(375+x)(275+x)=130500

We move all terms to the left:

(375+x)(275+x)-(130500)=0

We add all the numbers together, and all the variables

(x+375)(x+275)-130500=0

We multiply parentheses ..

(+x^2+275x+375x+103125)-130500=0

We get rid of parentheses

x^2+275x+375x+103125-130500=0

We add all the numbers together, and all the variables

x^2+650x-27375=0

a = 1; b = 650; c = -27375;
Δ = b2-4ac
Δ = 6502-4·1·(-27375)
Δ = 532000
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:

$\sqrt{\Delta}=\sqrt{532000}=\sqrt{400*1330}=\sqrt{400}*\sqrt{1330}=20\sqrt{1330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(650)-20\sqrt{1330}}{2*1}=\frac{-650-20\sqrt{1330}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(650)+20\sqrt{1330}}{2*1}=\frac{-650+20\sqrt{1330}}{2}
$