9x-4/x=2

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

9x-4/x=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


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}
$