0=75+30t-4.9t^2

Solution for 0=75+30t-4.9t^2 equation:

0=75+30t-4.9t^2

We move all terms to the left:

0-(75+30t-4.9t^2)=0

We add all the numbers together, and all the variables

-(75+30t-4.9t^2)=0

We get rid of parentheses

4.9t^2-30t-75=0

a = 4.9; b = -30; c = -75;
Δ = b2-4ac
Δ = -302-4·4.9·(-75)
Δ = 2370
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-\sqrt{2370}}{2*4.9}=\frac{30-\sqrt{2370}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{2370}}{2*4.9}=\frac{30+\sqrt{2370}}{9.8}
$