0=-3t^2+75t+37.5

Solution for 0=-3t^2+75t+37.5 equation:

0=-3t^2+75t+37.5

We move all terms to the left:

0-(-3t^2+75t+37.5)=0

We add all the numbers together, and all the variables

-(-3t^2+75t+37.5)=0

We get rid of parentheses

3t^2-75t-37.5=0

a = 3; b = -75; c = -37.5;
Δ = b2-4ac
Δ = -752-4·3·(-37.5)
Δ = 6075
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:

$\sqrt{\Delta}=\sqrt{6075}=\sqrt{2025*3}=\sqrt{2025}*\sqrt{3}=45\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-45\sqrt{3}}{2*3}=\frac{75-45\sqrt{3}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+45\sqrt{3}}{2*3}=\frac{75+45\sqrt{3}}{6}
$