x^2-25x=116

Solution for x^2-25x=116 equation:

x^2-25x=116

We move all terms to the left:

x^2-25x-(116)=0

a = 1; b = -25; c = -116;
Δ = b2-4ac
Δ = -252-4·1·(-116)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-33}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+33}{2*1}=\frac{58}{2}
=29
$