t=-4.9t^2+19,6t+58.8

Solution for t=-4.9t^2+19,6t+58.8 equation:

t=-4.9t^2+19.6t+58.8

We move all terms to the left:

t-(-4.9t^2+19.6t+58.8)=0

We get rid of parentheses

4.9t^2-19.6t+t-58.8=0

We add all the numbers together, and all the variables

4.9t^2-18.6t-58.8=0

a = 4.9; b = -18.6; c = -58.8;
Δ = b2-4ac
Δ = -18.62-4·4.9·(-58.8)
Δ = 1498.44
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{-(-18.6)-\sqrt{1498.44}}{2*4.9}=\frac{18.6-\sqrt{1498.44}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.6)+\sqrt{1498.44}}{2*4.9}=\frac{18.6+\sqrt{1498.44}}{9.8}
$