8/9x=8+4/4x

Solution for 8/9x=8+4/4x equation:

8/9x=8+4/4x

We move all terms to the left:

8/9x-(8+4/4x)=0


Domain of the equation: 9x!=0

x!=0/9

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

8/9x-(4/4x+8)=0

We get rid of parentheses

8/9x-4/4x-8=0

We calculate fractions


32x/36x^2+(-36x)/36x^2-8=0

We multiply all the terms by the denominator


32x+(-36x)-8*36x^2=0

Wy multiply elements

-288x^2+32x+(-36x)=0

We get rid of parentheses

-288x^2+32x-36x=0

We add all the numbers together, and all the variables

-288x^2-4x=0

a = -288; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-288)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-288}=\frac{0}{-576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-288}=\frac{8}{-576}
=-1/72
$