4/4x=4/2x-9*4

Solution for 4/4x=4/2x-9*4 equation:

4/4x=4/2x-9*4

We move all terms to the left:

4/4x-(4/2x-9*4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-9*4)!=0

x∈R


We add all the numbers together, and all the variables

4/4x-(4/2x-36)=0

We get rid of parentheses

4/4x-4/2x+36=0

We calculate fractions


8x/8x^2+(-16x)/8x^2+36=0

We multiply all the terms by the denominator


8x+(-16x)+36*8x^2=0

Wy multiply elements

288x^2+8x+(-16x)=0

We get rid of parentheses

288x^2+8x-16x=0

We add all the numbers together, and all the variables

288x^2-8x=0

a = 288; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·288·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*288}=\frac{0}{576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*288}=\frac{16}{576}
=1/36
$