2-6x=5x(x-1)

Solution for 2-6x=5x(x-1) equation:

2-6x=5x(x-1)

We move all terms to the left:

2-6x-(5x(x-1))=0


We calculate terms in parentheses: -(5x(x-1)), so:

5x(x-1)

We multiply parentheses

5x^2-5x

Back to the equation:

-(5x^2-5x)


We get rid of parentheses

-5x^2-6x+5x+2=0

We add all the numbers together, and all the variables

-5x^2-1x+2=0

a = -5; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-5)·2
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{-(-1)-\sqrt{41}}{2*-5}=\frac{1-\sqrt{41}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*-5}=\frac{1+\sqrt{41}}{-10}
$