3/5x+2/7x=-1

Solution for 3/5x+2/7x=-1 equation:

3/5x+2/7x=-1

We move all terms to the left:

3/5x+2/7x-(-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 add all the numbers together, and all the variables

3/5x+2/7x+1=0

We calculate fractions


21x/35x^2+10x/35x^2+1=0

We multiply all the terms by the denominator


21x+10x+1*35x^2=0

We add all the numbers together, and all the variables

31x+1*35x^2=0

Wy multiply elements

35x^2+31x=0

a = 35; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·35·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*35}=\frac{-62}{70}
=-31/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*35}=\frac{0}{70}
=0
$