1/3x+2=7x

Solution for 1/3x+2=7x equation:

1/3x+2=7x

We move all terms to the left:

1/3x+2-(7x)=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+2=0

We multiply all the terms by the denominator


-7x*3x+2*3x+1=0

Wy multiply elements

-21x^2+6x+1=0

a = -21; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-21)·1
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{30}}{2*-21}=\frac{-6-2\sqrt{30}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{30}}{2*-21}=\frac{-6+2\sqrt{30}}{-42}
$