1/5x+3/7x=10

Solution for 1/5x+3/7x=10 equation:

1/5x+3/7x=10

We move all terms to the left:

1/5x+3/7x-(10)=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


7x/35x^2+15x/35x^2-10=0

We multiply all the terms by the denominator


7x+15x-10*35x^2=0

We add all the numbers together, and all the variables

22x-10*35x^2=0

Wy multiply elements

-350x^2+22x=0

a = -350; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-350)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-350}=\frac{-44}{-700}
=11/175
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-350}=\frac{0}{-700}
=0
$