9x-3/x=2

Solution for 9x-3/x=2 equation:

9x-3/x=2

We move all terms to the left:

9x-3/x-(2)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


9x*x-2*x-3=0

We add all the numbers together, and all the variables

-2x+9x*x-3=0

Wy multiply elements

9x^2-2x-3=0

a = 9; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·9·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*9}=\frac{2-4\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*9}=\frac{2+4\sqrt{7}}{18}
$