7=2+13t-5t^2

Solution for 7=2+13t-5t^2 equation:

7=2+13t-5t^2

We move all terms to the left:

7-(2+13t-5t^2)=0

We get rid of parentheses

5t^2-13t-2+7=0

We add all the numbers together, and all the variables

5t^2-13t+5=0

a = 5; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·5·5
Δ = 69
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{69}}{2*5}=\frac{13-\sqrt{69}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{69}}{2*5}=\frac{13+\sqrt{69}}{10}
$