x^2+13x-30=9

Solution for x^2+13x-30=9 equation:

x^2+13x-30=9

We move all terms to the left:

x^2+13x-30-(9)=0

We add all the numbers together, and all the variables

x^2+13x-39=0

a = 1; b = 13; c = -39;
Δ = b2-4ac
Δ = 132-4·1·(-39)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5\sqrt{13}}{2*1}=\frac{-13-5\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5\sqrt{13}}{2*1}=\frac{-13+5\sqrt{13}}{2}
$