0=-4t^2+75t+50

Solution for 0=-4t^2+75t+50 equation:

0=-4t^2+75t+50

We move all terms to the left:

0-(-4t^2+75t+50)=0

We add all the numbers together, and all the variables

-(-4t^2+75t+50)=0

We get rid of parentheses

4t^2-75t-50=0

a = 4; b = -75; c = -50;
Δ = b2-4ac
Δ = -752-4·4·(-50)
Δ = 6425
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:

$\sqrt{\Delta}=\sqrt{6425}=\sqrt{25*257}=\sqrt{25}*\sqrt{257}=5\sqrt{257}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{257}}{2*4}=\frac{75-5\sqrt{257}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{257}}{2*4}=\frac{75+5\sqrt{257}}{8}
$