0=t^2-13t-2

Solution for 0=t^2-13t-2 equation:

0=t^2-13t-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-t^2+13t+2=0

We add all the numbers together, and all the variables

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

a = -1; b = 13; c = +2;
Δ = b2-4ac
Δ = 132-4·(-1)·2
Δ = 177
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{177}}{2*-1}=\frac{-13-\sqrt{177}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{177}}{2*-1}=\frac{-13+\sqrt{177}}{-2}
$