X=-5x^2+10x+20

Solution for X=-5x^2+10x+20 equation:

X=-5X^2+10X+20

We move all terms to the left:

X-(-5X^2+10X+20)=0

We get rid of parentheses

5X^2-10X+X-20=0

We add all the numbers together, and all the variables

5X^2-9X-20=0

a = 5; b = -9; c = -20;
Δ = b2-4ac
Δ = -92-4·5·(-20)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{481}}{2*5}=\frac{9-\sqrt{481}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{481}}{2*5}=\frac{9+\sqrt{481}}{10}
$