3x(2x-9)=2x-1

Solution for 3x(2x-9)=2x-1 equation:

3x(2x-9)=2x-1

We move all terms to the left:

3x(2x-9)-(2x-1)=0

We multiply parentheses

6x^2-27x-(2x-1)=0

We get rid of parentheses

6x^2-27x-2x+1=0

We add all the numbers together, and all the variables

6x^2-29x+1=0

a = 6; b = -29; c = +1;
Δ = b2-4ac
Δ = -292-4·6·1
Δ = 817
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{-(-29)-\sqrt{817}}{2*6}=\frac{29-\sqrt{817}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{817}}{2*6}=\frac{29+\sqrt{817}}{12}
$