x^2+5x-13=8

Solution for x^2+5x-13=8 equation:

x^2+5x-13=8

We move all terms to the left:

x^2+5x-13-(8)=0

We add all the numbers together, and all the variables

x^2+5x-21=0

a = 1; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·1·(-21)
Δ = 109
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{-(5)-\sqrt{109}}{2*1}=\frac{-5-\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{109}}{2*1}=\frac{-5+\sqrt{109}}{2}
$