6/6x+8/x=3

Solution for 6/6x+8/x=3 equation:

6/6x+8/x=3

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


6x/6x^2+48x/6x^2-3=0

We multiply all the terms by the denominator


6x+48x-3*6x^2=0

We add all the numbers together, and all the variables

54x-3*6x^2=0

Wy multiply elements

-18x^2+54x=0

a = -18; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-18)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-18}=\frac{-108}{-36}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-18}=\frac{0}{-36}
=0
$