(9+9x)/4x=x

Solution for (9+9x)/4x=x equation:

(9+9x)/4x=x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(9x+9)/4x=0

We multiply all the terms by the denominator


-1x*4x+(9x+9)=0

Wy multiply elements

-4x^2+(9x+9)=0

We get rid of parentheses

-4x^2+9x+9=0

a = -4; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·(-4)·9
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*-4}=\frac{6}{-8}
=-3/4
$