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}
$