-16t^2+35t+6=24

Solution for -16t^2+35t+6=24 equation:

-16t^2+35t+6=24

We move all terms to the left:

-16t^2+35t+6-(24)=0

We add all the numbers together, and all the variables

-16t^2+35t-18=0

a = -16; b = 35; c = -18;
Δ = b2-4ac
Δ = 352-4·(-16)·(-18)
Δ = 73
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{-(35)-\sqrt{73}}{2*-16}=\frac{-35-\sqrt{73}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{73}}{2*-16}=\frac{-35+\sqrt{73}}{-32}
$