80=1.76t^2-13.32t+41.00

Solution for 80=1.76t^2-13.32t+41.00 equation:

80=1.76t^2-13.32t+41.00

We move all terms to the left:

80-(1.76t^2-13.32t+41.00)=0

We get rid of parentheses

-1.76t^2+13.32t-41.00+80=0

We add all the numbers together, and all the variables

-1.76t^2+13.32t+39=0

a = -1.76; b = 13.32; c = +39;
Δ = b2-4ac
Δ = 13.322-4·(-1.76)·39
Δ = 451.9824
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{-(13.32)-\sqrt{451.9824}}{2*-1.76}=\frac{-13.32-\sqrt{451.9824}}{-3.52}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13.32)+\sqrt{451.9824}}{2*-1.76}=\frac{-13.32+\sqrt{451.9824}}{-3.52}
$