3/x-7=6x

Solution for 3/x-7=6x equation:

3/x-7=6x

We move all terms to the left:

3/x-7-(6x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+3/x-7=0

We multiply all the terms by the denominator


-6x*x-7*x+3=0

We add all the numbers together, and all the variables

-7x-6x*x+3=0

Wy multiply elements

-6x^2-7x+3=0

a = -6; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·(-6)·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*-6}=\frac{-4}{-12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*-6}=\frac{18}{-12}
=-1+1/2
$