1/(6x-4)=5x

Solution for 1/(6x-4)=5x equation:

1/(6x-4)=5x

We move all terms to the left:

1/(6x-4)-(5x)=0


Domain of the equation: (6x-4)!=0

We move all terms containing x to the left, all other terms to the right

6x!=4

x!=4/6

x!=2/3

x∈R


We add all the numbers together, and all the variables

-5x+1/(6x-4)=0

We multiply all the terms by the denominator


-5x*(6x-4)+1=0

We multiply parentheses

-30x^2+20x+1=0

a = -30; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·(-30)·1
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{130}}{2*-30}=\frac{-20-2\sqrt{130}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{130}}{2*-30}=\frac{-20+2\sqrt{130}}{-60}
$