4/x-3=9x

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

4/x-3=9x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x+4/x-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -9; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-9)·4
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*-9}=\frac{3-3\sqrt{17}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*-9}=\frac{3+3\sqrt{17}}{-18}
$