2x+5=x^2+8x-22

Solution for 2x+5=x^2+8x-22 equation:

2x+5=x^2+8x-22

We move all terms to the left:

2x+5-(x^2+8x-22)=0

We get rid of parentheses

-x^2+2x-8x+22+5=0

We add all the numbers together, and all the variables

-1x^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
$