152=0.5t^2

Solution for 152=0.5t^2 equation:

152=0.5t^2

We move all terms to the left:

152-(0.5t^2)=0

We get rid of parentheses

-0.5t^2+152=0

a = -0.5; b = 0; c = +152;
Δ = b2-4ac
Δ = 02-4·(-0.5)·152
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*-0.5}=\frac{0-4\sqrt{19}}{-1}
=-\frac{4\sqrt{19}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*-0.5}=\frac{0+4\sqrt{19}}{-1}
=\frac{4\sqrt{19}}{-1}
$