1.5*y^2-174.225*y=0

Solution for 1.5*y^2-174.225*y=0 equation:

1.5y^2-174.225y=0

a = 1.5; b = -174.225; c = 0;
Δ = b2-4ac
Δ = -174.2252-4·1.5·0
Δ = 30354.350625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-174.225)-\sqrt{30354.350625}}{2*1.5}=\frac{174.225-\sqrt{30354.350625}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-174.225)+\sqrt{30354.350625}}{2*1.5}=\frac{174.225+\sqrt{30354.350625}}{3}
$