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

Solution for 8(x-1)=(x-2)x-x equation:

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((x-2)x-x), so:

(x-2)x-x

We add all the numbers together, and all the variables

-1x+(x-2)x

We multiply parentheses

x^2-1x-2x

We add all the numbers together, and all the variables

x^2-3x

Back to the equation:

-(x^2-3x)


We get rid of parentheses

-x^2+8x+3x-8=0

We add all the numbers together, and all the variables

-1x^2+11x-8=0

a = -1; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·(-1)·(-8)
Δ = 89
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{-(11)-\sqrt{89}}{2*-1}=\frac{-11-\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{89}}{2*-1}=\frac{-11+\sqrt{89}}{-2}
$