x(3x-2)=1

Solution for x(3x-2)=1 equation:

x(3x-2)=1

We move all terms to the left:

x(3x-2)-(1)=0

We multiply parentheses

3x^2-2x-1=0

a = 3; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·3·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*3}=\frac{6}{6}
=1
$