0=-9.8t^2+5t+11

Solution for 0=-9.8t^2+5t+11 equation:

0=-9.8t^2+5t+11

We move all terms to the left:

0-(-9.8t^2+5t+11)=0

We add all the numbers together, and all the variables

-(-9.8t^2+5t+11)=0

We get rid of parentheses

9.8t^2-5t-11=0

a = 9.8; b = -5; c = -11;
Δ = b2-4ac
Δ = -52-4·9.8·(-11)
Δ = 456.2
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{-(-5)-\sqrt{456.2}}{2*9.8}=\frac{5-\sqrt{456.2}}{19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{456.2}}{2*9.8}=\frac{5+\sqrt{456.2}}{19.6}
$