5/x-9=9/4x-6

Solution for 5/x-9=9/4x-6 equation:

5/x-9=9/4x-6

We move all terms to the left:

5/x-9-(9/4x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

5/x-9/4x+6-9=0

We calculate fractions


20x/4x^2+(-9x)/4x^2+6-9=0

We add all the numbers together, and all the variables

20x/4x^2+(-9x)/4x^2-3=0

We multiply all the terms by the denominator


20x+(-9x)-3*4x^2=0

Wy multiply elements

-12x^2+20x+(-9x)=0

We get rid of parentheses

-12x^2+20x-9x=0

We add all the numbers together, and all the variables

-12x^2+11x=0

a = -12; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-12)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-12}=\frac{-22}{-24}
=11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-12}=\frac{0}{-24}
=0
$