1.5t^2=50

Solution for 1.5t^2=50 equation:

1.5t^2=50

We move all terms to the left:

1.5t^2-(50)=0

a = 1.5; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·1.5·(-50)
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*1.5}=\frac{0-10\sqrt{3}}{3}
=-\frac{10\sqrt{3}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*1.5}=\frac{0+10\sqrt{3}}{3}
=\frac{10\sqrt{3}}{3}
$