5/8x+35=5/7x

Solution for 5/8x+35=5/7x equation:

5/8x+35=5/7x

We move all terms to the left:

5/8x+35-(5/7x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-(+5/7x)+35=0

We get rid of parentheses

5/8x-5/7x+35=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

1960x^2+35x+(-40x)=0

We get rid of parentheses

1960x^2+35x-40x=0

We add all the numbers together, and all the variables

1960x^2-5x=0

a = 1960; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1960·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1960}=\frac{0}{3920}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1960}=\frac{10}{3920}
=1/392
$