x^2+13x-7=15

Solution for x^2+13x-7=15 equation:

x^2+13x-7=15

We move all terms to the left:

x^2+13x-7-(15)=0

We add all the numbers together, and all the variables

x^2+13x-22=0

a = 1; b = 13; c = -22;
Δ = b2-4ac
Δ = 132-4·1·(-22)
Δ = 257
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{257}}{2*1}=\frac{-13-\sqrt{257}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{257}}{2*1}=\frac{-13+\sqrt{257}}{2}
$