-16t^2+140t+75=0

Solution for -16t^2+140t+75=0 equation:

-16t^2+140t+75=0

a = -16; b = 140; c = +75;
Δ = b2-4ac
Δ = 1402-4·(-16)·75
Δ = 24400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24400}=\sqrt{400*61}=\sqrt{400}*\sqrt{61}=20\sqrt{61}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-20\sqrt{61}}{2*-16}=\frac{-140-20\sqrt{61}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+20\sqrt{61}}{2*-16}=\frac{-140+20\sqrt{61}}{-32}
$