8=1+13t-5t^2

Solution for 8=1+13t-5t^2 equation:

8=1+13t-5t^2

We move all terms to the left:

8-(1+13t-5t^2)=0

We get rid of parentheses

5t^2-13t-1+8=0

We add all the numbers together, and all the variables

5t^2-13t+7=0

a = 5; b = -13; c = +7;
Δ = b2-4ac
Δ = -132-4·5·7
Δ = 29
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{-(-13)-\sqrt{29}}{2*5}=\frac{13-\sqrt{29}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{29}}{2*5}=\frac{13+\sqrt{29}}{10}
$