2x/4x+2*14x+7/6=x/6

Solution for 2x/4x+2*14x+7/6=x/6 equation:

2x/4x+2*14x+7/6=x/6

We move all terms to the left:

2x/4x+2*14x+7/6-(x/6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x/4x+2*14x-(+x/6)+7/6=0

Wy multiply elements

2x/4x+28x-(+x/6)+7/6=0

We get rid of parentheses

2x/4x+28x-x/6+7/6=0

We calculate fractions


28x+12x/24x+27x/24x=0

We multiply all the terms by the denominator


28x*24x+12x+27x=0

We add all the numbers together, and all the variables

39x+28x*24x=0

Wy multiply elements

672x^2+39x=0

a = 672; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·672·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*672}=\frac{-78}{1344}
=-13/224
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*672}=\frac{0}{1344}
=0
$