8/2x-4=5/9x-9

Solution for 8/2x-4=5/9x-9 equation:

8/2x-4=5/9x-9

We move all terms to the left:

8/2x-4-(5/9x-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

8/2x-5/9x+9-4=0

We calculate fractions


72x/18x^2+(-10x)/18x^2+9-4=0

We add all the numbers together, and all the variables

72x/18x^2+(-10x)/18x^2+5=0

We multiply all the terms by the denominator


72x+(-10x)+5*18x^2=0

Wy multiply elements

90x^2+72x+(-10x)=0

We get rid of parentheses

90x^2+72x-10x=0

We add all the numbers together, and all the variables

90x^2+62x=0

a = 90; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·90·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*90}=\frac{-124}{180}
=-31/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*90}=\frac{0}{180}
=0
$