5/2x+3/7x=1

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

5/2x+3/7x=1

We move all terms to the left:

5/2x+3/7x-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


35x/14x^2+6x/14x^2-1=0

We multiply all the terms by the denominator


35x+6x-1*14x^2=0

We add all the numbers together, and all the variables

41x-1*14x^2=0

Wy multiply elements

-14x^2+41x=0

a = -14; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-14)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-14}=\frac{-82}{-28}
=2+13/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-14}=\frac{0}{-28}
=0
$