-25t^2+75t+24=0

Solution for -25t^2+75t+24=0 equation:

-25t^2+75t+24=0

a = -25; b = 75; c = +24;
Δ = b2-4ac
Δ = 752-4·(-25)·24
Δ = 8025
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:

$\sqrt{\Delta}=\sqrt{8025}=\sqrt{25*321}=\sqrt{25}*\sqrt{321}=5\sqrt{321}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-5\sqrt{321}}{2*-25}=\frac{-75-5\sqrt{321}}{-50}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+5\sqrt{321}}{2*-25}=\frac{-75+5\sqrt{321}}{-50}
$