6/x=2+2x

Solution for 6/x=2+2x equation:

6/x=2+2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6/x-2x-2=0

We multiply all the terms by the denominator


-2x*x-2*x+6=0

We add all the numbers together, and all the variables

-2x-2x*x+6=0

Wy multiply elements

-2x^2-2x+6=0

a = -2; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-2)·6
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-2}=\frac{2-2\sqrt{13}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-2}=\frac{2+2\sqrt{13}}{-4}
$