6+3x/2x=2x/6

Solution for 6+3x/2x=2x/6 equation:

6+3x/2x=2x/6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-4x^2)/12x+18x/12x+6=0

We multiply all the terms by the denominator


(-4x^2)+18x+6*12x=0

Wy multiply elements

(-4x^2)+18x+72x=0

We get rid of parentheses

-4x^2+18x+72x=0

We add all the numbers together, and all the variables

-4x^2+90x=0

a = -4; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-4)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-4}=\frac{-180}{-8}
=22+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-4}=\frac{0}{-8}
=0
$