X(x-25)=116

Solution for X(x-25)=116 equation:

X(X-25)=116

We move all terms to the left:

X(X-25)-(116)=0

We multiply parentheses

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
$