81=12t+5t^2

Solution for 81=12t+5t^2 equation:

81=12t+5t^2

We move all terms to the left:

81-(12t+5t^2)=0

We get rid of parentheses

-5t^2-12t+81=0

a = -5; b = -12; c = +81;
Δ = b2-4ac
Δ = -122-4·(-5)·81
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-42}{2*-5}=\frac{-30}{-10}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+42}{2*-5}=\frac{54}{-10}
=-5+2/5
$