4/x-2=9x

Solution for 4/x-2=9x equation:

4/x-2=9x

We move all terms to the left:

4/x-2-(9x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x+4/x-2=0

We multiply all the terms by the denominator


-9x*x-2*x+4=0

We add all the numbers together, and all the variables

-2x-9x*x+4=0

Wy multiply elements

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

a = -9; b = -2; c = +4;
Δ = b2-4ac
Δ = -22-4·(-9)·4
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{37}}{2*-9}=\frac{2-2\sqrt{37}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{37}}{2*-9}=\frac{2+2\sqrt{37}}{-18}
$