(x+75)(40+x)=96000

Solution for (x+75)(40+x)=96000 equation:

(x+75)(40+x)=96000

We move all terms to the left:

(x+75)(40+x)-(96000)=0

We add all the numbers together, and all the variables

(x+75)(x+40)-96000=0

We multiply parentheses ..

(+x^2+40x+75x+3000)-96000=0

We get rid of parentheses

x^2+40x+75x+3000-96000=0

We add all the numbers together, and all the variables

x^2+115x-93000=0

a = 1; b = 115; c = -93000;
Δ = b2-4ac
Δ = 1152-4·1·(-93000)
Δ = 385225
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:

$\sqrt{\Delta}=\sqrt{385225}=\sqrt{25*15409}=\sqrt{25}*\sqrt{15409}=5\sqrt{15409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-5\sqrt{15409}}{2*1}=\frac{-115-5\sqrt{15409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+5\sqrt{15409}}{2*1}=\frac{-115+5\sqrt{15409}}{2}
$