x^2-13=-5x

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

x^2-13=-5x

We move all terms to the left:

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

We get rid of parentheses

x^2+5x-13=0

a = 1; b = 5; c = -13;
Δ = b2-4ac
Δ = 52-4·1·(-13)
Δ = 77
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{77}}{2*1}=\frac{-5-\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{77}}{2*1}=\frac{-5+\sqrt{77}}{2}
$