1.5x^2=1000

Solution for 1.5x^2=1000 equation:

1.5x^2=1000

We move all terms to the left:

1.5x^2-(1000)=0

a = 1.5; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·1.5·(-1000)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*1.5}=\frac{0-20\sqrt{15}}{3}
=-\frac{20\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*1.5}=\frac{0+20\sqrt{15}}{3}
=\frac{20\sqrt{15}}{3}
$