0=-16t^2+150t+162

Solution for 0=-16t^2+150t+162 equation:

0=-16t^2+150t+162

We move all terms to the left:

0-(-16t^2+150t+162)=0

We add all the numbers together, and all the variables

-(-16t^2+150t+162)=0

We get rid of parentheses

16t^2-150t-162=0

a = 16; b = -150; c = -162;
Δ = b2-4ac
Δ = -1502-4·16·(-162)
Δ = 32868
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:

$\sqrt{\Delta}=\sqrt{32868}=\sqrt{36*913}=\sqrt{36}*\sqrt{913}=6\sqrt{913}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-6\sqrt{913}}{2*16}=\frac{150-6\sqrt{913}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+6\sqrt{913}}{2*16}=\frac{150+6\sqrt{913}}{32}
$