X^2-13x=108

Solution for X^2-13x=108 equation:

X^2-13X=108

We move all terms to the left:

X^2-13X-(108)=0

a = 1; b = -13; c = -108;
Δ = b2-4ac
Δ = -132-4·1·(-108)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{601}}{2*1}=\frac{13-\sqrt{601}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{601}}{2*1}=\frac{13+\sqrt{601}}{2}
$