4/x+2=6x-2

Solution for 4/x+2=6x-2 equation:

4/x+2=6x-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-6x+2+2=0

We multiply all the terms by the denominator


-6x*x+2*x+2*x+4=0

We add all the numbers together, and all the variables

4x-6x*x+4=0

Wy multiply elements

-6x^2+4x+4=0

a = -6; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-6)·4
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-6}=\frac{-4-4\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-6}=\frac{-4+4\sqrt{7}}{-12}
$