8/x-1+9/2x+1=7/2x+1

Solution for 8/x-1+9/2x+1=7/2x+1 equation:

8/x-1+9/2x+1=7/2x+1

We move all terms to the left:

8/x-1+9/2x+1-(7/2x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

8/x+9/2x-(7/2x+1)=0

We get rid of parentheses

8/x+9/2x-7/2x-1=0

We calculate fractions


16x/2x^2+(-7x+9)/2x^2-1=0

We multiply all the terms by the denominator


16x+(-7x+9)-1*2x^2=0

Wy multiply elements

-2x^2+16x+(-7x+9)=0

We get rid of parentheses

-2x^2+16x-7x+9=0

We add all the numbers together, and all the variables

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

a = -2; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·(-2)·9
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-2}=\frac{-9-3\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-2}=\frac{-9+3\sqrt{17}}{-4}
$