X2+20x=-23

Solution for X2+20x=-23 equation:

X2+20X=-23

We move all terms to the left:

X2+20X-(-23)=0

We add all the numbers together, and all the variables

X^2+20X+23=0

a = 1; b = 20; c = +23;
Δ = b2-4ac
Δ = 202-4·1·23
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{77}}{2*1}=\frac{-20-2\sqrt{77}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{77}}{2*1}=\frac{-20+2\sqrt{77}}{2}
$