3+1/7x=x

Solution for 3+1/7x=x equation:

3+1/7x=x

We move all terms to the left:

3+1/7x-(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

-1x+1/7x+3=0

We multiply all the terms by the denominator


-1x*7x+3*7x+1=0

Wy multiply elements

-7x^2+21x+1=0

a = -7; b = 21; c = +1;
Δ = b2-4ac
Δ = 212-4·(-7)·1
Δ = 469
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{469}}{2*-7}=\frac{-21-\sqrt{469}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{469}}{2*-7}=\frac{-21+\sqrt{469}}{-14}
$