2x(x-4)=x-1

Solution for 2x(x-4)=x-1 equation:

2x(x-4)=x-1

We move all terms to the left:

2x(x-4)-(x-1)=0

We multiply parentheses

2x^2-8x-(x-1)=0

We get rid of parentheses

2x^2-8x-x+1=0

We add all the numbers together, and all the variables

2x^2-9x+1=0

a = 2; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·2·1
Δ = 73
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{73}}{2*2}=\frac{9-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{73}}{2*2}=\frac{9+\sqrt{73}}{4}
$