t=16t^2+91t+5.5

Solution for t=16t^2+91t+5.5 equation:

t=16t^2+91t+5.5

We move all terms to the left:

t-(16t^2+91t+5.5)=0

We get rid of parentheses

-16t^2+t-91t-5.5=0

We add all the numbers together, and all the variables

-16t^2-90t-5.5=0

a = -16; b = -90; c = -5.5;
Δ = b2-4ac
Δ = -902-4·(-16)·(-5.5)
Δ = 7748
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:

$\sqrt{\Delta}=\sqrt{7748}=\sqrt{4*1937}=\sqrt{4}*\sqrt{1937}=2\sqrt{1937}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1937}}{2*-16}=\frac{90-2\sqrt{1937}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1937}}{2*-16}=\frac{90+2\sqrt{1937}}{-32}
$