t=-16t^2+24t+2

Solution for t=-16t^2+24t+2 equation:

t=-16t^2+24t+2

We move all terms to the left:

t-(-16t^2+24t+2)=0

We get rid of parentheses

16t^2-24t+t-2=0

We add all the numbers together, and all the variables

16t^2-23t-2=0

a = 16; b = -23; c = -2;
Δ = b2-4ac
Δ = -232-4·16·(-2)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3\sqrt{73}}{2*16}=\frac{23-3\sqrt{73}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3\sqrt{73}}{2*16}=\frac{23+3\sqrt{73}}{32}
$