x^2+15x=-2x-66

Solution for x^2+15x=-2x-66 equation:

x^2+15x=-2x-66

We move all terms to the left:

x^2+15x-(-2x-66)=0

We get rid of parentheses

x^2+15x+2x+66=0

We add all the numbers together, and all the variables

x^2+17x+66=0

a = 1; b = 17; c = +66;
Δ = b2-4ac
Δ = 172-4·1·66
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-5}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+5}{2*1}=\frac{-12}{2}
=-6
$