x^2+36x=-73

Solution for x^2+36x=-73 equation:

x^2+36x=-73

We move all terms to the left:

x^2+36x-(-73)=0

We add all the numbers together, and all the variables

x^2+36x+73=0

a = 1; b = 36; c = +73;
Δ = b2-4ac
Δ = 362-4·1·73
Δ = 1004
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:

$\sqrt{\Delta}=\sqrt{1004}=\sqrt{4*251}=\sqrt{4}*\sqrt{251}=2\sqrt{251}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{251}}{2*1}=\frac{-36-2\sqrt{251}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{251}}{2*1}=\frac{-36+2\sqrt{251}}{2}
$