165=16t^2+101+30

Solution for 165=16t^2+101+30 equation:

165=16t^2+101+30

We move all terms to the left:

165-(16t^2+101+30)=0

We get rid of parentheses

-16t^2-101-30+165=0

We add all the numbers together, and all the variables

-16t^2+34=0

a = -16; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-16)·34
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{34}}{2*-16}=\frac{0-8\sqrt{34}}{-32}
=-\frac{8\sqrt{34}}{-32}
=-\frac{\sqrt{34}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{34}}{2*-16}=\frac{0+8\sqrt{34}}{-32}
=\frac{8\sqrt{34}}{-32}
=\frac{\sqrt{34}}{-4}
$