(2x-2)+(x+1)+x(+x+1)=(2x-9)+(x+1)+(x+8)+x

Solution for (2x-2)+(x+1)+x(+x+1)=(2x-9)+(x+1)+(x+8)+x equation:

(2x-2)+(x+1)+x(+x+1)=(2x-9)+(x+1)+(x+8)+x

We move all terms to the left:

(2x-2)+(x+1)+x(+x+1)-((2x-9)+(x+1)+(x+8)+x)=0

We add all the numbers together, and all the variables

(2x-2)+(x+1)+x(x+1)-((2x-9)+(x+1)+(x+8)+x)=0

We multiply parentheses

x^2+(2x-2)+(x+1)+x-((2x-9)+(x+1)+(x+8)+x)=0

We get rid of parentheses

x^2+2x+x+x-((2x-9)+(x+1)+(x+8)+x)-2+1=0


We calculate terms in parentheses: -((2x-9)+(x+1)+(x+8)+x), so:

(2x-9)+(x+1)+(x+8)+x

We add all the numbers together, and all the variables

x+(2x-9)+(x+1)+(x+8)

We get rid of parentheses

x+2x+x+x-9+1+8

We add all the numbers together, and all the variables

5x

Back to the equation:

-(5x)


We add all the numbers together, and all the variables

x^2-1x-1=0

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