4x^2+36x=-10

Solution for 4x^2+36x=-10 equation:

4x^2+36x=-10

We move all terms to the left:

4x^2+36x-(-10)=0

We add all the numbers together, and all the variables

4x^2+36x+10=0

a = 4; b = 36; c = +10;
Δ = b2-4ac
Δ = 362-4·4·10
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{71}}{2*4}=\frac{-36-4\sqrt{71}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{71}}{2*4}=\frac{-36+4\sqrt{71}}{8}
$