3/7x+6=2+x

Solution for 3/7x+6=2+x equation:

3/7x+6=2+x

We move all terms to the left:

3/7x+6-(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

3/7x-(x+2)+6=0

We get rid of parentheses

3/7x-x-2+6=0

We multiply all the terms by the denominator


-x*7x-2*7x+6*7x+3=0

Wy multiply elements

-7x^2-14x+42x+3=0

We add all the numbers together, and all the variables

-7x^2+28x+3=0

a = -7; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·(-7)·3
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{217}}{2*-7}=\frac{-28-2\sqrt{217}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{217}}{2*-7}=\frac{-28+2\sqrt{217}}{-14}
$