1/2x-9=9+5/4x

Solution for 1/2x-9=9+5/4x equation:

1/2x-9=9+5/4x

We move all terms to the left:

1/2x-9-(9+5/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(5/4x+9)-9=0

We get rid of parentheses

1/2x-5/4x-9-9=0

We calculate fractions


4x/8x^2+(-10x)/8x^2-9-9=0

We add all the numbers together, and all the variables

4x/8x^2+(-10x)/8x^2-18=0

We multiply all the terms by the denominator


4x+(-10x)-18*8x^2=0

Wy multiply elements

-144x^2+4x+(-10x)=0

We get rid of parentheses

-144x^2+4x-10x=0

We add all the numbers together, and all the variables

-144x^2-6x=0

a = -144; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-144)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-144}=\frac{12}{-288}
=-1/24
$