x^2+15x=-9

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

x^2+15x=-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2+15x+9=0

a = 1; b = 15; c = +9;
Δ = b2-4ac
Δ = 152-4·1·9
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{21}}{2*1}=\frac{-15-3\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{21}}{2*1}=\frac{-15+3\sqrt{21}}{2}
$