292.5=5*x^2+20*x

Solution for 292.5=5*x^2+20*x equation:

292.5=5x^2+20x

We move all terms to the left:

292.5-(5x^2+20x)=0

We get rid of parentheses

-5x^2-20x+292.5=0

a = -5; b = -20; c = +292.5;
Δ = b2-4ac
Δ = -202-4·(-5)·292.5
Δ = 6250
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:

$\sqrt{\Delta}=\sqrt{6250}=\sqrt{625*10}=\sqrt{625}*\sqrt{10}=25\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-25\sqrt{10}}{2*-5}=\frac{20-25\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+25\sqrt{10}}{2*-5}=\frac{20+25\sqrt{10}}{-10}
$