t=-4.9t^2+24.5t+1

Solution for t=-4.9t^2+24.5t+1 equation:

t=-4.9t^2+24.5t+1

We move all terms to the left:

t-(-4.9t^2+24.5t+1)=0

We get rid of parentheses

4.9t^2-24.5t+t-1=0

We add all the numbers together, and all the variables

4.9t^2-23.5t-1=0

a = 4.9; b = -23.5; c = -1;
Δ = b2-4ac
Δ = -23.52-4·4.9·(-1)
Δ = 571.85
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{-(-23.5)-\sqrt{571.85}}{2*4.9}=\frac{23.5-\sqrt{571.85}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23.5)+\sqrt{571.85}}{2*4.9}=\frac{23.5+\sqrt{571.85}}{9.8}
$