1.5y^2=400

Solution for 1.5y^2=400 equation:

1.5y^2=400

We move all terms to the left:

1.5y^2-(400)=0

a = 1.5; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·1.5·(-400)
Δ = 2400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*1.5}=\frac{0-20\sqrt{6}}{3}
=-\frac{20\sqrt{6}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*1.5}=\frac{0+20\sqrt{6}}{3}
=\frac{20\sqrt{6}}{3}
$