3t^2-3t-2=166

Solution for 3t^2-3t-2=166 equation:

3t^2-3t-2=166

We move all terms to the left:

3t^2-3t-2-(166)=0

We add all the numbers together, and all the variables

3t^2-3t-168=0

a = 3; b = -3; c = -168;
Δ = b2-4ac
Δ = -32-4·3·(-168)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*3}=\frac{-42}{6}
=-7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*3}=\frac{48}{6}
=8
$