3/x+2=6x-4x+8

Solution for 3/x+2=6x-4x+8 equation:

3/x+2=6x-4x+8

We move all terms to the left:

3/x+2-(6x-4x+8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(2x+8)+2=0

We get rid of parentheses

3/x-2x-8+2=0

We multiply all the terms by the denominator


-2x*x-8*x+2*x+3=0

We add all the numbers together, and all the variables

-6x-2x*x+3=0

Wy multiply elements

-2x^2-6x+3=0

a = -2; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-2)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*-2}=\frac{6-2\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*-2}=\frac{6+2\sqrt{15}}{-4}
$