7/6x+2=7/2x

Solution for 7/6x+2=7/2x equation:

7/6x+2=7/2x

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


14x/12x^2+(-42x)/12x^2+2=0

We multiply all the terms by the denominator


14x+(-42x)+2*12x^2=0

Wy multiply elements

24x^2+14x+(-42x)=0

We get rid of parentheses

24x^2+14x-42x=0

We add all the numbers together, and all the variables

24x^2-28x=0

a = 24; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·24·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*24}=\frac{56}{48}
=1+1/6
$