9=0.5t2

Solution for 9=0.5t2 equation:

9=0.5t^2

We move all terms to the left:

9-(0.5t^2)=0

We get rid of parentheses

-0.5t^2+9=0

a = -0.5; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-0.5)·9
Δ = 18
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:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*-0.5}=\frac{0-3\sqrt{2}}{-1}
=-\frac{3\sqrt{2}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*-0.5}=\frac{0+3\sqrt{2}}{-1}
=\frac{3\sqrt{2}}{-1}
$