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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-7x+1=0

a = 2; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·2·1
Δ = 41
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{-(-7)-\sqrt{41}}{2*2}=\frac{7-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{41}}{2*2}=\frac{7+\sqrt{41}}{4}
$