-x^2-20=8x-5

Solution for -x^2-20=8x-5 equation:

-x^2-20=8x-5

We move all terms to the left:

-x^2-20-(8x-5)=0

We add all the numbers together, and all the variables

-1x^2-(8x-5)-20=0

We get rid of parentheses

-1x^2-8x+5-20=0

We add all the numbers together, and all the variables

-1x^2-8x-15=0

a = -1; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·(-1)·(-15)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*-1}=\frac{6}{-2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*-1}=\frac{10}{-2}
=-5
$