t=-11t^2+44t+80

Solution for t=-11t^2+44t+80 equation:

t=-11t^2+44t+80

We move all terms to the left:

t-(-11t^2+44t+80)=0

We get rid of parentheses

11t^2-44t+t-80=0

We add all the numbers together, and all the variables

11t^2-43t-80=0

a = 11; b = -43; c = -80;
Δ = b2-4ac
Δ = -432-4·11·(-80)
Δ = 5369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{5369}}{2*11}=\frac{43-\sqrt{5369}}{22}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{5369}}{2*11}=\frac{43+\sqrt{5369}}{22}
$