x^2+96x=116

Solution for x^2+96x=116 equation:

x^2+96x=116

We move all terms to the left:

x^2+96x-(116)=0

a = 1; b = 96; c = -116;
Δ = b2-4ac
Δ = 962-4·1·(-116)
Δ = 9680
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:

$\sqrt{\Delta}=\sqrt{9680}=\sqrt{1936*5}=\sqrt{1936}*\sqrt{5}=44\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-44\sqrt{5}}{2*1}=\frac{-96-44\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+44\sqrt{5}}{2*1}=\frac{-96+44\sqrt{5}}{2}
$