-x^2+20x-23=0

Solution for -x^2+20x-23=0 equation:

-x^2+20x-23=0

We add all the numbers together, and all the variables

-1x^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}
$