500=1.5x^2

Solution for 500=1.5x^2 equation:

500=1.5x^2

We move all terms to the left:

500-(1.5x^2)=0

We get rid of parentheses

-1.5x^2+500=0

a = -1.5; b = 0; c = +500;
Δ = b2-4ac
Δ = 02-4·(-1.5)·500
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{30}}{2*-1.5}=\frac{0-10\sqrt{30}}{-3}
=-\frac{10\sqrt{30}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{30}}{2*-1.5}=\frac{0+10\sqrt{30}}{-3}
=\frac{10\sqrt{30}}{-3}
$