0=-4.9t^2+14.2t+75

Solution for 0=-4.9t^2+14.2t+75 equation:

0=-4.9t^2+14.2t+75

We move all terms to the left:

0-(-4.9t^2+14.2t+75)=0

We add all the numbers together, and all the variables

-(-4.9t^2+14.2t+75)=0

We get rid of parentheses

4.9t^2-14.2t-75=0

a = 4.9; b = -14.2; c = -75;
Δ = b2-4ac
Δ = -14.22-4·4.9·(-75)
Δ = 1671.64
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{-(-14.2)-\sqrt{1671.64}}{2*4.9}=\frac{14.2-\sqrt{1671.64}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.2)+\sqrt{1671.64}}{2*4.9}=\frac{14.2+\sqrt{1671.64}}{9.8}
$