6/x=4x-1

Solution for 6/x=4x-1 equation:

6/x=4x-1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6/x-4x+1=0

We multiply all the terms by the denominator


-4x*x+1*x+6=0

We add all the numbers together, and all the variables

x-4x*x+6=0

Wy multiply elements

-4x^2+x+6=0

a = -4; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-4)·6
Δ = 97
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{-(1)-\sqrt{97}}{2*-4}=\frac{-1-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-4}=\frac{-1+\sqrt{97}}{-8}
$