-4.5t^2+4.5=2

Solution for -4.5t^2+4.5=2 equation:

-4.5t^2+4.5=2

We move all terms to the left:

-4.5t^2+4.5-(2)=0

We add all the numbers together, and all the variables

-4.5t^2+2.5=0

a = -4.5; b = 0; c = +2.5;
Δ = b2-4ac
Δ = 02-4·(-4.5)·2.5
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{5}}{2*-4.5}=\frac{0-3\sqrt{5}}{-9}
=-\frac{3\sqrt{5}}{-9}
=-\frac{\sqrt{5}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{5}}{2*-4.5}=\frac{0+3\sqrt{5}}{-9}
=\frac{3\sqrt{5}}{-9}
=\frac{\sqrt{5}}{-3}
$