3/x-9=4x

Solution for 3/x-9=4x equation:

3/x-9=4x

We move all terms to the left:

3/x-9-(4x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+3/x-9=0

We multiply all the terms by the denominator


-4x*x-9*x+3=0

We add all the numbers together, and all the variables

-9x-4x*x+3=0

Wy multiply elements

-4x^2-9x+3=0

a = -4; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-4)·3
Δ = 129
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{-(-9)-\sqrt{129}}{2*-4}=\frac{9-\sqrt{129}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*-4}=\frac{9+\sqrt{129}}{-8}
$