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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

2x^2-2x-3x+1=0

We add all the numbers together, and all the variables

2x^2-5x+1=0

a = 2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·2·1
Δ = 17
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{-(-5)-\sqrt{17}}{2*2}=\frac{5-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*2}=\frac{5+\sqrt{17}}{4}
$