2x-6/x=9

Solution for 2x-6/x=9 equation:

2x-6/x=9

We move all terms to the left:

2x-6/x-(9)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-9*x-6=0

We add all the numbers together, and all the variables

-9x+2x*x-6=0

Wy multiply elements

2x^2-9x-6=0

a = 2; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·2·(-6)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{129}}{2*2}=\frac{9-\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*2}=\frac{9+\sqrt{129}}{4}
$