x^2+20x=-87

Solution for x^2+20x=-87 equation:

x^2+20x=-87

We move all terms to the left:

x^2+20x-(-87)=0

We add all the numbers together, and all the variables

x^2+20x+87=0

a = 1; b = 20; c = +87;
Δ = b2-4ac
Δ = 202-4·1·87
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{13}}{2*1}=\frac{-20-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{13}}{2*1}=\frac{-20+2\sqrt{13}}{2}
$