4/x-7=6x

Solution for 4/x-7=6x equation:

4/x-7=6x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+4/x-7=0

We multiply all the terms by the denominator


-6x*x-7*x+4=0

We add all the numbers together, and all the variables

-7x-6x*x+4=0

Wy multiply elements

-6x^2-7x+4=0

a = -6; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-6)·4
Δ = 145
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{-(-7)-\sqrt{145}}{2*-6}=\frac{7-\sqrt{145}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*-6}=\frac{7+\sqrt{145}}{-12}
$