X2+20x+61=0

Solution for X2+20x+61=0 equation:

X2+20X+61=0

We add all the numbers together, and all the variables

X^2+20X+61=0

a = 1; b = 20; c = +61;
Δ = b2-4ac
Δ = 202-4·1·61
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{39}}{2*1}=\frac{-20-2\sqrt{39}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{39}}{2*1}=\frac{-20+2\sqrt{39}}{2}
$