x*2x=500

Solution for x*2x=500 equation:

x*2x=500

We move all terms to the left:

x*2x-(500)=0

Wy multiply elements

2x^2-500=0

a = 2; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·2·(-500)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*2}=\frac{0-20\sqrt{10}}{4}
=-\frac{20\sqrt{10}}{4}
=-5\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*2}=\frac{0+20\sqrt{10}}{4}
=\frac{20\sqrt{10}}{4}
=5\sqrt{10}
$