4x-2=2/11x

Solution for 4x-2=2/11x equation:

4x-2=2/11x

We move all terms to the left:

4x-2-(2/11x)=0


Domain of the equation: 11x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+2/11x)-2=0

We get rid of parentheses

4x-2/11x-2=0

We multiply all the terms by the denominator


4x*11x-2*11x-2=0

Wy multiply elements

44x^2-22x-2=0

a = 44; b = -22; c = -2;
Δ = b2-4ac
Δ = -222-4·44·(-2)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{209}}{2*44}=\frac{22-2\sqrt{209}}{88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{209}}{2*44}=\frac{22+2\sqrt{209}}{88}
$