0=-15x^2+110x+500

Solution for 0=-15x^2+110x+500 equation:

0=-15x^2+110x+500

We move all terms to the left:

0-(-15x^2+110x+500)=0

We add all the numbers together, and all the variables

-(-15x^2+110x+500)=0

We get rid of parentheses

15x^2-110x-500=0

a = 15; b = -110; c = -500;
Δ = b2-4ac
Δ = -1102-4·15·(-500)
Δ = 42100
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:

$\sqrt{\Delta}=\sqrt{42100}=\sqrt{100*421}=\sqrt{100}*\sqrt{421}=10\sqrt{421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-10\sqrt{421}}{2*15}=\frac{110-10\sqrt{421}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+10\sqrt{421}}{2*15}=\frac{110+10\sqrt{421}}{30}
$