t=92t-16t^2

Solution for t=92t-16t^2 equation:

t=92t-16t^2

We move all terms to the left:

t-(92t-16t^2)=0

We get rid of parentheses

16t^2-92t+t=0

We add all the numbers together, and all the variables

16t^2-91t=0

a = 16; b = -91; c = 0;
Δ = b2-4ac
Δ = -912-4·16·0
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-91}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+91}{2*16}=\frac{182}{32}
=5+11/16
$