0=-4.5t^2-18t+15

Solution for 0=-4.5t^2-18t+15 equation:

0=-4.5t^2-18t+15

We move all terms to the left:

0-(-4.5t^2-18t+15)=0

We add all the numbers together, and all the variables

-(-4.5t^2-18t+15)=0

We get rid of parentheses

4.5t^2+18t-15=0

a = 4.5; b = 18; c = -15;
Δ = b2-4ac
Δ = 182-4·4.5·(-15)
Δ = 594
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:

$\sqrt{\Delta}=\sqrt{594}=\sqrt{9*66}=\sqrt{9}*\sqrt{66}=3\sqrt{66}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-3\sqrt{66}}{2*4.5}=\frac{-18-3\sqrt{66}}{9}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+3\sqrt{66}}{2*4.5}=\frac{-18+3\sqrt{66}}{9}
$