9/8x=8+4/9x

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

9/8x=8+4/9x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


81x/72x^2+(-32x)/72x^2-8=0

We multiply all the terms by the denominator


81x+(-32x)-8*72x^2=0

Wy multiply elements

-576x^2+81x+(-32x)=0

We get rid of parentheses

-576x^2+81x-32x=0

We add all the numbers together, and all the variables

-576x^2+49x=0

a = -576; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-576)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-576}=\frac{-98}{-1152}
=49/576
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-576}=\frac{0}{-1152}
=0
$