6x(3x-1)=14

Solution for 6x(3x-1)=14 equation:

6x(3x-1)=14

We move all terms to the left:

6x(3x-1)-(14)=0

We multiply parentheses

18x^2-6x-14=0

a = 18; b = -6; c = -14;
Δ = b2-4ac
Δ = -62-4·18·(-14)
Δ = 1044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{29}}{2*18}=\frac{6-6\sqrt{29}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{29}}{2*18}=\frac{6+6\sqrt{29}}{36}
$