150=-16t^2+116t+101

Solution for 150=-16t^2+116t+101 equation:

150=-16t^2+116t+101

We move all terms to the left:

150-(-16t^2+116t+101)=0

We get rid of parentheses

16t^2-116t-101+150=0

We add all the numbers together, and all the variables

16t^2-116t+49=0

a = 16; b = -116; c = +49;
Δ = b2-4ac
Δ = -1162-4·16·49
Δ = 10320
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:

$\sqrt{\Delta}=\sqrt{10320}=\sqrt{16*645}=\sqrt{16}*\sqrt{645}=4\sqrt{645}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{645}}{2*16}=\frac{116-4\sqrt{645}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{645}}{2*16}=\frac{116+4\sqrt{645}}{32}
$