1/x=9/2x-6

Solution for 1/x=9/2x-6 equation:

1/x=9/2x-6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

1/x-9/2x+6=0

We calculate fractions


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

We multiply all the terms by the denominator


2x+(-9x)+6*2x^2=0

Wy multiply elements

12x^2+2x+(-9x)=0

We get rid of parentheses

12x^2+2x-9x=0

We add all the numbers together, and all the variables

12x^2-7x=0

a = 12; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·12·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*12}=\frac{14}{24}
=7/12
$