8=3+11t-5t^2

Solution for 8=3+11t-5t^2 equation:

8=3+11t-5t^2

We move all terms to the left:

8-(3+11t-5t^2)=0

We get rid of parentheses

5t^2-11t-3+8=0

We add all the numbers together, and all the variables

5t^2-11t+5=0

a = 5; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·5·5
Δ = 21
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{-(-11)-\sqrt{21}}{2*5}=\frac{11-\sqrt{21}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{21}}{2*5}=\frac{11+\sqrt{21}}{10}
$