3/5x+5/7x=1

Solution for 3/5x+5/7x=1 equation:

3/5x+5/7x=1

We move all terms to the left:

3/5x+5/7x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


21x/35x^2+25x/35x^2-1=0

We multiply all the terms by the denominator


21x+25x-1*35x^2=0

We add all the numbers together, and all the variables

46x-1*35x^2=0

Wy multiply elements

-35x^2+46x=0

a = -35; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-35)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-35}=\frac{-92}{-70}
=1+11/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-35}=\frac{0}{-70}
=0
$