-16t^2+88t=120

Solution for -16t^2+88t=120 equation:

-16t^2+88t=120

We move all terms to the left:

-16t^2+88t-(120)=0

a = -16; b = 88; c = -120;
Δ = b2-4ac
Δ = 882-4·(-16)·(-120)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-8}{2*-16}=\frac{-96}{-32}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+8}{2*-16}=\frac{-80}{-32}
=2+1/2
$