6/7x=2+x

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

6/7x=2+x

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6/7x-x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-7x^2-14x+6=0

a = -7; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·(-7)·6
Δ = 364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{91}}{2*-7}=\frac{14-2\sqrt{91}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{91}}{2*-7}=\frac{14+2\sqrt{91}}{-14}
$