5/8x-7=32/9x+8

Solution for 5/8x-7=32/9x+8 equation:

5/8x-7=32/9x+8

We move all terms to the left:

5/8x-7-(32/9x+8)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 9x+8)!=0

x∈R


We get rid of parentheses

5/8x-32/9x-8-7=0

We calculate fractions


45x/72x^2+(-256x)/72x^2-8-7=0

We add all the numbers together, and all the variables

45x/72x^2+(-256x)/72x^2-15=0

We multiply all the terms by the denominator


45x+(-256x)-15*72x^2=0

Wy multiply elements

-1080x^2+45x+(-256x)=0

We get rid of parentheses

-1080x^2+45x-256x=0

We add all the numbers together, and all the variables

-1080x^2-211x=0

a = -1080; b = -211; c = 0;
Δ = b2-4ac
Δ = -2112-4·(-1080)·0
Δ = 44521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44521}=211$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-211)-211}{2*-1080}=\frac{0}{-2160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-211)+211}{2*-1080}=\frac{422}{-2160}
=-211/1080
$