165=-16t^2+117t+30

Solution for 165=-16t^2+117t+30 equation:

165=-16t^2+117t+30

We move all terms to the left:

165-(-16t^2+117t+30)=0

We get rid of parentheses

16t^2-117t-30+165=0

We add all the numbers together, and all the variables

16t^2-117t+135=0

a = 16; b = -117; c = +135;
Δ = b2-4ac
Δ = -1172-4·16·135
Δ = 5049
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:

$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-3\sqrt{561}}{2*16}=\frac{117-3\sqrt{561}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+3\sqrt{561}}{2*16}=\frac{117+3\sqrt{561}}{32}
$