3t+1t+132t2=72

Solution for 3t+1t+132t2=72 equation:

3t+1t+132t^2=72

We move all terms to the left:

3t+1t+132t^2-(72)=0

We add all the numbers together, and all the variables

132t^2+4t-72=0

a = 132; b = 4; c = -72;
Δ = b2-4ac
Δ = 42-4·132·(-72)
Δ = 38032
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{38032}=\sqrt{16*2377}=\sqrt{16}*\sqrt{2377}=4\sqrt{2377}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2377}}{2*132}=\frac{-4-4\sqrt{2377}}{264}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2377}}{2*132}=\frac{-4+4\sqrt{2377}}{264}
$