-16t^2+75t+40=0

Solution for -16t^2+75t+40=0 equation:

-16t^2+75t+40=0

a = -16; b = 75; c = +40;
Δ = b2-4ac
Δ = 752-4·(-16)·40
Δ = 8185
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{-(75)-\sqrt{8185}}{2*-16}=\frac{-75-\sqrt{8185}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{8185}}{2*-16}=\frac{-75+\sqrt{8185}}{-32}
$