6/x+8=9/2x+1

Solution for 6/x+8=9/2x+1 equation:

6/x+8=9/2x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/2x^2+(-9x)/2x^2-1+8=0

We add all the numbers together, and all the variables

12x/2x^2+(-9x)/2x^2+7=0

We multiply all the terms by the denominator


12x+(-9x)+7*2x^2=0

Wy multiply elements

14x^2+12x+(-9x)=0

We get rid of parentheses

14x^2+12x-9x=0

We add all the numbers together, and all the variables

14x^2+3x=0

a = 14; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·14·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*14}=\frac{-6}{28}
=-3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*14}=\frac{0}{28}
=0
$