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

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

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


((x-2)-x*x)-3*x)=0


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

(x-2)-x*x

Wy multiply elements

-1x^2+(x-2)

We get rid of parentheses

-1x^2+x-2

Back to the equation:

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


Wy multiply elements

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

We get rid of parentheses

-1x^2+x-3x-2=0

We add all the numbers together, and all the variables

-1x^2-2x-2=0

a = -1; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·(-1)·(-2)
Δ = -4
Delta is less than zero, so there is no solution for the equation