-16t^2+80t=51

Solution for -16t^2+80t=51 equation:

-16t^2+80t=51

We move all terms to the left:

-16t^2+80t-(51)=0

a = -16; b = 80; c = -51;
Δ = b2-4ac
Δ = 802-4·(-16)·(-51)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-56}{2*-16}=\frac{-136}{-32}
=4+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+56}{2*-16}=\frac{-24}{-32}
=3/4
$