1/2x+8=5/9x

Solution for 1/2x+8=5/9x equation:

1/2x+8=5/9x

We move all terms to the left:

1/2x+8-(5/9x)=0


Domain of the equation: 2x!=0

x!=0/2

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

1/2x-(+5/9x)+8=0

We get rid of parentheses

1/2x-5/9x+8=0

We calculate fractions


9x/18x^2+(-10x)/18x^2+8=0

We multiply all the terms by the denominator


9x+(-10x)+8*18x^2=0

Wy multiply elements

144x^2+9x+(-10x)=0

We get rid of parentheses

144x^2+9x-10x=0

We add all the numbers together, and all the variables

144x^2-1x=0

a = 144; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·144·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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