4x^2+36x=-9

Solution for 4x^2+36x=-9 equation:

4x^2+36x=-9

We move all terms to the left:

4x^2+36x-(-9)=0

We add all the numbers together, and all the variables

4x^2+36x+9=0

a = 4; b = 36; c = +9;
Δ = b2-4ac
Δ = 362-4·4·9
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-24\sqrt{2}}{2*4}=\frac{-36-24\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+24\sqrt{2}}{2*4}=\frac{-36+24\sqrt{2}}{8}
$