t=-16t^2+162

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

t=-16t^2+162

We move all terms to the left:

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

We get rid of parentheses

16t^2+t-162=0

a = 16; b = 1; c = -162;
Δ = b2-4ac
Δ = 12-4·16·(-162)
Δ = 10369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{10369}}{2*16}=\frac{-1-\sqrt{10369}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{10369}}{2*16}=\frac{-1+\sqrt{10369}}{32}
$