0=-16t^2+30t+9

Solution for 0=-16t^2+30t+9 equation:

0=-16t^2+30t+9

We move all terms to the left:

0-(-16t^2+30t+9)=0

We add all the numbers together, and all the variables

-(-16t^2+30t+9)=0

We get rid of parentheses

16t^2-30t-9=0

a = 16; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·16·(-9)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{41}}{2*16}=\frac{30-6\sqrt{41}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{41}}{2*16}=\frac{30+6\sqrt{41}}{32}
$