(x+8/7x)+1=x-5/x

Solution for (x+8/7x)+1=x-5/x equation:

(x+8/7x)+1=x-5/x

We move all terms to the left:

(x+8/7x)+1-(x-5/x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+x+8/7x)-(+x-5/x)+1=0

We get rid of parentheses

x+8/7x-x+5/x+1=0

We calculate fractions


x-x+8x/7x^2+35x/7x^2+1=0

We add all the numbers together, and all the variables

8x/7x^2+35x/7x^2+1=0

We multiply all the terms by the denominator


8x+35x+1*7x^2=0

We add all the numbers together, and all the variables

43x+1*7x^2=0

Wy multiply elements

7x^2+43x=0

a = 7; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·7·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*7}=\frac{-86}{14}
=-6+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*7}=\frac{0}{14}
=0
$