x+8/5x+7=x+8/7x+5

Solution for x+8/5x+7=x+8/7x+5 equation:

x+8/5x+7=x+8/7x+5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


x-x+56x/35x^2+(-40x)/35x^2-5+7=0

We add all the numbers together, and all the variables

56x/35x^2+(-40x)/35x^2+2=0

We multiply all the terms by the denominator


56x+(-40x)+2*35x^2=0

Wy multiply elements

70x^2+56x+(-40x)=0

We get rid of parentheses

70x^2+56x-40x=0

We add all the numbers together, and all the variables

70x^2+16x=0

a = 70; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·70·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*70}=\frac{-32}{140}
=-8/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*70}=\frac{0}{140}
=0
$