a^2+20a+90=0

Solution for a^2+20a+90=0 equation:

a^2+20a+90=0

a = 1; b = 20; c = +90;
Δ = b2-4ac
Δ = 202-4·1·90
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{10}}{2*1}=\frac{-20-2\sqrt{10}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{10}}{2*1}=\frac{-20+2\sqrt{10}}{2}
$