150=-16t^2+118t+2

Solution for 150=-16t^2+118t+2 equation:

150=-16t^2+118t+2

We move all terms to the left:

150-(-16t^2+118t+2)=0

We get rid of parentheses

16t^2-118t-2+150=0

We add all the numbers together, and all the variables

16t^2-118t+148=0

a = 16; b = -118; c = +148;
Δ = b2-4ac
Δ = -1182-4·16·148
Δ = 4452
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:

$\sqrt{\Delta}=\sqrt{4452}=\sqrt{4*1113}=\sqrt{4}*\sqrt{1113}=2\sqrt{1113}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-2\sqrt{1113}}{2*16}=\frac{118-2\sqrt{1113}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+2\sqrt{1113}}{2*16}=\frac{118+2\sqrt{1113}}{32}
$