X^2+20x+81=-10

Solution for X^2+20x+81=-10 equation:

X^2+20X+81=-10

We move all terms to the left:

X^2+20X+81-(-10)=0

We add all the numbers together, and all the variables

X^2+20X+91=0

a = 1; b = 20; c = +91;
Δ = b2-4ac
Δ = 202-4·1·91
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6}{2*1}=\frac{-26}{2}
=-13
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6}{2*1}=\frac{-14}{2}
=-7
$