9x-4/x=3

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

9x-4/x=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


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}
$