3(2x-3)x=1

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

3(2x-3)x=1

We move all terms to the left:

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

We multiply parentheses

6x^2-9x-1=0

a = 6; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·6·(-1)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*6}=\frac{9-\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*6}=\frac{9+\sqrt{105}}{12}
$