x^2+8x=-5x-30

Solution for x^2+8x=-5x-30 equation:

x^2+8x=-5x-30

We move all terms to the left:

x^2+8x-(-5x-30)=0

We get rid of parentheses

x^2+8x+5x+30=0

We add all the numbers together, and all the variables

x^2+13x+30=0

a = 1; b = 13; c = +30;
Δ = b2-4ac
Δ = 132-4·1·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*1}=\frac{-6}{2}
=-3
$