1/3x-7x=3

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

1/3x-7x=3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-21x^2-9x+1=0

a = -21; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-21)·1
Δ = 165
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{-(-9)-\sqrt{165}}{2*-21}=\frac{9-\sqrt{165}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{165}}{2*-21}=\frac{9+\sqrt{165}}{-42}
$