x^2+20x+22=0

Solution for x^2+20x+22=0 equation:

x^2+20x+22=0

a = 1; b = 20; c = +22;
Δ = b2-4ac
Δ = 202-4·1·22
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{78}}{2*1}=\frac{-20-2\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{78}}{2*1}=\frac{-20+2\sqrt{78}}{2}
$