2x^2+12x+15=-8x+9

Solution for 2x^2+12x+15=-8x+9 equation:

2x^2+12x+15=-8x+9

We move all terms to the left:

2x^2+12x+15-(-8x+9)=0

We get rid of parentheses

2x^2+12x+8x-9+15=0

We add all the numbers together, and all the variables

2x^2+20x+6=0

a = 2; b = 20; c = +6;
Δ = b2-4ac
Δ = 202-4·2·6
Δ = 352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{22}}{2*2}=\frac{-20-4\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{22}}{2*2}=\frac{-20+4\sqrt{22}}{4}
$