-37.5=15t-4.9t^2

Solution for -37.5=15t-4.9t^2 equation:

-37.5=15t-4.9t^2

We move all terms to the left:

-37.5-(15t-4.9t^2)=0

We get rid of parentheses

4.9t^2-15t-37.5=0

a = 4.9; b = -15; c = -37.5;
Δ = b2-4ac
Δ = -152-4·4.9·(-37.5)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-8\sqrt{15}}{2*4.9}=\frac{15-8\sqrt{15}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+8\sqrt{15}}{2*4.9}=\frac{15+8\sqrt{15}}{9.8}
$