1/2x+2/6x=1+2/7

Solution for 1/2x+2/6x=1+2/7 equation:

1/2x+2/6x=1+2/7

We move all terms to the left:

1/2x+2/6x-(1+2/7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+2/6x-(2/7+1)=0

We get rid of parentheses

1/2x+2/6x-1-2/7=0

We calculate fractions


(-144x^2)/588x^2+294x/588x^2+196x/588x^2-1=0

We multiply all the terms by the denominator


(-144x^2)+294x+196x-1*588x^2=0

We add all the numbers together, and all the variables

(-144x^2)+490x-1*588x^2=0

Wy multiply elements

(-144x^2)-588x^2+490x=0

We get rid of parentheses

-144x^2-588x^2+490x=0

We add all the numbers together, and all the variables

-732x^2+490x=0

a = -732; b = 490; c = 0;
Δ = b2-4ac
Δ = 4902-4·(-732)·0
Δ = 240100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{240100}=490$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(490)-490}{2*-732}=\frac{-980}{-1464}
=245/366
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(490)+490}{2*-732}=\frac{0}{-1464}
=0
$