x^2+15x+22=5x-2

Solution for x^2+15x+22=5x-2 equation:

x^2+15x+22=5x-2

We move all terms to the left:

x^2+15x+22-(5x-2)=0

We get rid of parentheses

x^2+15x-5x+2+22=0

We add all the numbers together, and all the variables

x^2+10x+24=0

a = 1; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*1}=\frac{-8}{2}
=-4
$