-500x(2x-9)=0

Solution for -500x(2x-9)=0 equation:

-500x(2x-9)=0

We multiply parentheses

-1000x^2+4500x=0

a = -1000; b = 4500; c = 0;
Δ = b2-4ac
Δ = 45002-4·(-1000)·0
Δ = 20250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20250000}=4500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4500)-4500}{2*-1000}=\frac{-9000}{-2000}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4500)+4500}{2*-1000}=\frac{0}{-2000}
=0
$