x^2-13x-30=30

Solution for x^2-13x-30=30 equation:

x^2-13x-30=30

We move all terms to the left:

x^2-13x-30-(30)=0

We add all the numbers together, and all the variables

x^2-13x-60=0

a = 1; b = -13; c = -60;
Δ = b2-4ac
Δ = -132-4·1·(-60)
Δ = 409
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{409}}{2*1}=\frac{13-\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{409}}{2*1}=\frac{13+\sqrt{409}}{2}
$