4/x-3=6x

Solution for 4/x-3=6x equation:

4/x-3=6x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+4/x-3=0

We multiply all the terms by the denominator


-6x*x-3*x+4=0

We add all the numbers together, and all the variables

-3x-6x*x+4=0

Wy multiply elements

-6x^2-3x+4=0

a = -6; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-6)·4
Δ = 105
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{-(-3)-\sqrt{105}}{2*-6}=\frac{3-\sqrt{105}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-6}=\frac{3+\sqrt{105}}{-12}
$