9x^2+12x=-1

Solution for 9x^2+12x=-1 equation:

9x^2+12x=-1

We move all terms to the left:

9x^2+12x-(-1)=0

We add all the numbers together, and all the variables

9x^2+12x+1=0

a = 9; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·9·1
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{3}}{2*9}=\frac{-12-6\sqrt{3}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{3}}{2*9}=\frac{-12+6\sqrt{3}}{18}
$