82=1.5t^2

Solution for 82=1.5t^2 equation:

82=1.5t^2

We move all terms to the left:

82-(1.5t^2)=0

We get rid of parentheses

-1.5t^2+82=0

a = -1.5; b = 0; c = +82;
Δ = b2-4ac
Δ = 02-4·(-1.5)·82
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{123}}{2*-1.5}=\frac{0-2\sqrt{123}}{-3}
=-\frac{2\sqrt{123}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{123}}{2*-1.5}=\frac{0+2\sqrt{123}}{-3}
=\frac{2\sqrt{123}}{-3}
$