(500)=2x2-6x

Solution for (500)=2x2-6x equation:

(500)=2x^2-6x

We move all terms to the left:

(500)-(2x^2-6x)=0

We get rid of parentheses

-2x^2+6x+500=0

a = -2; b = 6; c = +500;
Δ = b2-4ac
Δ = 62-4·(-2)·500
Δ = 4036
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:

$\sqrt{\Delta}=\sqrt{4036}=\sqrt{4*1009}=\sqrt{4}*\sqrt{1009}=2\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1009}}{2*-2}=\frac{-6-2\sqrt{1009}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1009}}{2*-2}=\frac{-6+2\sqrt{1009}}{-4}
$