x^2+20x+45=-10

Solution for x^2+20x+45=-10 equation:

x^2+20x+45=-10

We move all terms to the left:

x^2+20x+45-(-10)=0

We add all the numbers together, and all the variables

x^2+20x+55=0

a = 1; b = 20; c = +55;
Δ = b2-4ac
Δ = 202-4·1·55
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6\sqrt{5}}{2*1}=\frac{-20-6\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6\sqrt{5}}{2*1}=\frac{-20+6\sqrt{5}}{2}
$