x^2+15x+27=-2x+5

Solution for x^2+15x+27=-2x+5 equation:

x^2+15x+27=-2x+5

We move all terms to the left:

x^2+15x+27-(-2x+5)=0

We get rid of parentheses

x^2+15x+2x-5+27=0

We add all the numbers together, and all the variables

x^2+17x+22=0

a = 1; b = 17; c = +22;
Δ = b2-4ac
Δ = 172-4·1·22
Δ = 201
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{-(17)-\sqrt{201}}{2*1}=\frac{-17-\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{201}}{2*1}=\frac{-17+\sqrt{201}}{2}
$