x^2-1=5x+8

Solution for x^2-1=5x+8 equation:

x^2-1=5x+8

We move all terms to the left:

x^2-1-(5x+8)=0

We get rid of parentheses

x^2-5x-8-1=0

We add all the numbers together, and all the variables

x^2-5x-9=0

a = 1; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·1·(-9)
Δ = 61
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{61}}{2*1}=\frac{5-\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{61}}{2*1}=\frac{5+\sqrt{61}}{2}
$