t(3t-2)=14

Solution for t(3t-2)=14 equation:

t(3t-2)=14

We move all terms to the left:

t(3t-2)-(14)=0

We multiply parentheses

3t^2-2t-14=0

a = 3; b = -2; c = -14;
Δ = b2-4ac
Δ = -22-4·3·(-14)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*3}=\frac{2-2\sqrt{43}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*3}=\frac{2+2\sqrt{43}}{6}
$