2/x=9/8x+1

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

2/x=9/8x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


16x/8x^2+(-9x)/8x^2-1=0

We multiply all the terms by the denominator


16x+(-9x)-1*8x^2=0

Wy multiply elements

-8x^2+16x+(-9x)=0

We get rid of parentheses

-8x^2+16x-9x=0

We add all the numbers together, and all the variables

-8x^2+7x=0

a = -8; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-8)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-8}=\frac{-14}{-16}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-8}=\frac{0}{-16}
=0
$