(x+76)(40+x)=9120

Solution for (x+76)(40+x)=9120 equation:

(x+76)(40+x)=9120

We move all terms to the left:

(x+76)(40+x)-(9120)=0

We add all the numbers together, and all the variables

(x+76)(x+40)-9120=0

We multiply parentheses ..

(+x^2+40x+76x+3040)-9120=0

We get rid of parentheses

x^2+40x+76x+3040-9120=0

We add all the numbers together, and all the variables

x^2+116x-6080=0

a = 1; b = 116; c = -6080;
Δ = b2-4ac
Δ = 1162-4·1·(-6080)
Δ = 37776
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:

$\sqrt{\Delta}=\sqrt{37776}=\sqrt{16*2361}=\sqrt{16}*\sqrt{2361}=4\sqrt{2361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-4\sqrt{2361}}{2*1}=\frac{-116-4\sqrt{2361}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+4\sqrt{2361}}{2*1}=\frac{-116+4\sqrt{2361}}{2}
$