-1/3x+7=x

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

-1/3x+7=x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+21x-1=0

a = -3; b = 21; c = -1;
Δ = b2-4ac
Δ = 212-4·(-3)·(-1)
Δ = 429
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{429}}{2*-3}=\frac{-21-\sqrt{429}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{429}}{2*-3}=\frac{-21+\sqrt{429}}{-6}
$