t=-16t^2+10t+36

Solution for t=-16t^2+10t+36 equation:

t=-16t^2+10t+36

We move all terms to the left:

t-(-16t^2+10t+36)=0

We get rid of parentheses

16t^2-10t+t-36=0

We add all the numbers together, and all the variables

16t^2-9t-36=0

a = 16; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·16·(-36)
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{265}}{2*16}=\frac{9-3\sqrt{265}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{265}}{2*16}=\frac{9+3\sqrt{265}}{32}
$