4(x+1)+x=x(x-2)+2

Solution for 4(x+1)+x=x(x-2)+2 equation:

4(x+1)+x=x(x-2)+2

We move all terms to the left:

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

We add all the numbers together, and all the variables

x+4(x+1)-(x(x-2)+2)=0

We multiply parentheses

x+4x-(x(x-2)+2)+4=0


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

x(x-2)+2

We multiply parentheses

x^2-2x+2

Back to the equation:

-(x^2-2x+2)


We add all the numbers together, and all the variables

5x-(x^2-2x+2)+4=0

We get rid of parentheses

-x^2+5x+2x-2+4=0

We add all the numbers together, and all the variables

-1x^2+7x+2=0

a = -1; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·(-1)·2
Δ = 57
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{57}}{2*-1}=\frac{-7-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{57}}{2*-1}=\frac{-7+\sqrt{57}}{-2}
$