-16t^2+83t+4.5=0

Solution for -16t^2+83t+4.5=0 equation:

-16t^2+83t+4.5=0

a = -16; b = 83; c = +4.5;
Δ = b2-4ac
Δ = 832-4·(-16)·4.5
Δ = 7177
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{-(83)-\sqrt{7177}}{2*-16}=\frac{-83-\sqrt{7177}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+\sqrt{7177}}{2*-16}=\frac{-83+\sqrt{7177}}{-32}
$