5x+30=x^2-8

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

5x+30=x^2-8

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+5x+38=0

a = -1; b = 5; c = +38;
Δ = b2-4ac
Δ = 52-4·(-1)·38
Δ = 177
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{177}}{2*-1}=\frac{-5-\sqrt{177}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{177}}{2*-1}=\frac{-5+\sqrt{177}}{-2}
$