t=-4.9t^2+19.6+58.8

Solution for t=-4.9t^2+19.6+58.8 equation:

t=-4.9t^2+19.6+58.8

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4.9t^2+t-78.4=0

a = 4.9; b = 1; c = -78.4;
Δ = b2-4ac
Δ = 12-4·4.9·(-78.4)
Δ = 1537.64
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{-(1)-\sqrt{1537.64}}{2*4.9}=\frac{-1-\sqrt{1537.64}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1537.64}}{2*4.9}=\frac{-1+\sqrt{1537.64}}{9.8}
$