-x^2+10x+20=0

Solution for -x^2+10x+20=0 equation:

-x^2+10x+20=0

We add all the numbers together, and all the variables

-1x^2+10x+20=0

a = -1; b = 10; c = +20;
Δ = b2-4ac
Δ = 102-4·(-1)·20
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*-1}=\frac{-10-6\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*-1}=\frac{-10+6\sqrt{5}}{-2}
$