5/3x-7=x

Solution for 5/3x-7=x equation:

5/3x-7=x

We move all terms to the left:

5/3x-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+5/3x-7=0

We multiply all the terms by the denominator


-1x*3x-7*3x+5=0

Wy multiply elements

-3x^2-21x+5=0

a = -3; b = -21; c = +5;
Δ = b2-4ac
Δ = -212-4·(-3)·5
Δ = 501
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{501}}{2*-3}=\frac{21-\sqrt{501}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{501}}{2*-3}=\frac{21+\sqrt{501}}{-6}
$