x=-5x^2+20x+60

Solution for x=-5x^2+20x+60 equation:

x=-5x^2+20x+60

We move all terms to the left:

x-(-5x^2+20x+60)=0

We get rid of parentheses

5x^2-20x+x-60=0

We add all the numbers together, and all the variables

5x^2-19x-60=0

a = 5; b = -19; c = -60;
Δ = b2-4ac
Δ = -192-4·5·(-60)
Δ = 1561
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{-(-19)-\sqrt{1561}}{2*5}=\frac{19-\sqrt{1561}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1561}}{2*5}=\frac{19+\sqrt{1561}}{10}
$