(x-2)(2+x)/3=x

Solution for (x-2)(2+x)/3=x equation:

(x-2)(2+x)/3=x

We move all terms to the left:

(x-2)(2+x)/3-(x)=0

We add all the numbers together, and all the variables

(x-2)(x+2)/3-x=0

We add all the numbers together, and all the variables

-1x+(x-2)(x+2)/3=0

We use the square of the difference formula

x^2-1x-4=0

a = 1; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·1·(-4)
Δ = 17
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{17}}{2*1}=\frac{1-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*1}=\frac{1+\sqrt{17}}{2}
$