x^2-x-19=5x+8

Solution for x^2-x-19=5x+8 equation:

x^2-x-19=5x+8

We move all terms to the left:

x^2-x-19-(5x+8)=0

We add all the numbers together, and all the variables

x^2-1x-(5x+8)-19=0

We get rid of parentheses

x^2-1x-5x-8-19=0

We add all the numbers together, and all the variables

x^2-6x-27=0

a = 1; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*1}=\frac{18}{2}
=9
$