5x/x-1-9/7x-7=-8

Solution for 5x/x-1-9/7x-7=-8 equation:

5x/x-1-9/7x-7=-8

We move all terms to the left:

5x/x-1-9/7x-7-(-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5x/x-9/7x=0

We calculate fractions


35x^2/7x^2+(-9x)/7x^2=0

We multiply all the terms by the denominator


35x^2+(-9x)=0

We get rid of parentheses

35x^2-9x=0

a = 35; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·35·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*35}=\frac{0}{70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*35}=\frac{18}{70}
=9/35
$