(5)/x=9/8x+1

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

(5)/x=9/8x+1

We move all terms to the left:

(5)/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

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

We calculate fractions


40x/8x^2+(-9x)/8x^2-1=0

We multiply all the terms by the denominator


40x+(-9x)-1*8x^2=0

Wy multiply elements

-8x^2+40x+(-9x)=0

We get rid of parentheses

-8x^2+40x-9x=0

We add all the numbers together, and all the variables

-8x^2+31x=0

a = -8; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-8)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-8}=\frac{-62}{-16}
=3+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-8}=\frac{0}{-16}
=0
$