6=13t-5t^2

Solution for 6=13t-5t^2 equation:

6=13t-5t^2

We move all terms to the left:

6-(13t-5t^2)=0

We get rid of parentheses

5t^2-13t+6=0

a = 5; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·5·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*5}=\frac{6}{10}
=3/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*5}=\frac{20}{10}
=2
$