4x^2+36x=-29

Solution for 4x^2+36x=-29 equation:

4x^2+36x=-29

We move all terms to the left:

4x^2+36x-(-29)=0

We add all the numbers together, and all the variables

4x^2+36x+29=0

a = 4; b = 36; c = +29;
Δ = b2-4ac
Δ = 362-4·4·29
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{13}}{2*4}=\frac{-36-8\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{13}}{2*4}=\frac{-36+8\sqrt{13}}{8}
$