t=-16t^2+117t+2

Solution for t=-16t^2+117t+2 equation:

t=-16t^2+117t+2

We move all terms to the left:

t-(-16t^2+117t+2)=0

We get rid of parentheses

16t^2-117t+t-2=0

We add all the numbers together, and all the variables

16t^2-116t-2=0

a = 16; b = -116; c = -2;
Δ = b2-4ac
Δ = -1162-4·16·(-2)
Δ = 13584
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:

$\sqrt{\Delta}=\sqrt{13584}=\sqrt{16*849}=\sqrt{16}*\sqrt{849}=4\sqrt{849}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{849}}{2*16}=\frac{116-4\sqrt{849}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{849}}{2*16}=\frac{116+4\sqrt{849}}{32}
$