182=13t+t^2

Solution for 182=13t+t^2 equation:

182=13t+t^2

We move all terms to the left:

182-(13t+t^2)=0

We get rid of parentheses

-t^2-13t+182=0

We add all the numbers together, and all the variables

-1t^2-13t+182=0

a = -1; b = -13; c = +182;
Δ = b2-4ac
Δ = -132-4·(-1)·182
Δ = 897
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{897}}{2*-1}=\frac{13-\sqrt{897}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{897}}{2*-1}=\frac{13+\sqrt{897}}{-2}
$