1=7.78t-4.9t^2

Solution for 1=7.78t-4.9t^2 equation:

1=7.78t-4.9t^2

We move all terms to the left:

1-(7.78t-4.9t^2)=0

We get rid of parentheses

4.9t^2-7.78t+1=0

a = 4.9; b = -7.78; c = +1;
Δ = b2-4ac
Δ = -7.782-4·4.9·1
Δ = 40.9284
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{-(-7.78)-\sqrt{40.9284}}{2*4.9}=\frac{7.78-\sqrt{40.9284}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.78)+\sqrt{40.9284}}{2*4.9}=\frac{7.78+\sqrt{40.9284}}{9.8}
$