-16t^2+75t=81

Solution for -16t^2+75t=81 equation:

-16t^2+75t=81

We move all terms to the left:

-16t^2+75t-(81)=0

a = -16; b = 75; c = -81;
Δ = b2-4ac
Δ = 752-4·(-16)·(-81)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-21}{2*-16}=\frac{-96}{-32}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+21}{2*-16}=\frac{-54}{-32}
=1+11/16
$