442=4.5t^2

Solution for 442=4.5t^2 equation:

442=4.5t^2

We move all terms to the left:

442-(4.5t^2)=0

We get rid of parentheses

-4.5t^2+442=0

a = -4.5; b = 0; c = +442;
Δ = b2-4ac
Δ = 02-4·(-4.5)·442
Δ = 7956
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:

$\sqrt{\Delta}=\sqrt{7956}=\sqrt{36*221}=\sqrt{36}*\sqrt{221}=6\sqrt{221}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{221}}{2*-4.5}=\frac{0-6\sqrt{221}}{-9}
=-\frac{6\sqrt{221}}{-9}
=-\frac{2\sqrt{221}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{221}}{2*-4.5}=\frac{0+6\sqrt{221}}{-9}
=\frac{6\sqrt{221}}{-9}
=\frac{2\sqrt{221}}{-3}
$