15=-16t^2+30t+4.5

Solution for 15=-16t^2+30t+4.5 equation:

15=-16t^2+30t+4.5

We move all terms to the left:

15-(-16t^2+30t+4.5)=0

We get rid of parentheses

16t^2-30t-4.5+15=0

We add all the numbers together, and all the variables

16t^2-30t+10.5=0

a = 16; b = -30; c = +10.5;
Δ = b2-4ac
Δ = -302-4·16·10.5
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{57}}{2*16}=\frac{30-2\sqrt{57}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{57}}{2*16}=\frac{30+2\sqrt{57}}{32}
$