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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2-1x+6x-6)), so:

(+x^2-1x+6x-6)

We get rid of parentheses

x^2-1x+6x-6

We add all the numbers together, and all the variables

x^2+5x-6

Back to the equation:

-(x^2+5x-6)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-10x+11=0

a = -1; b = -10; c = +11;
Δ = b2-4ac
Δ = -102-4·(-1)·11
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-12}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+12}{2*-1}=\frac{22}{-2}
=-11
$