x/3x=5/7x-13

Solution for x/3x=5/7x-13 equation:

x/3x=5/7x-13

We move all terms to the left:

x/3x-(5/7x-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x-13)!=0

x∈R


We get rid of parentheses

x/3x-5/7x+13=0

We calculate fractions


7x^2/21x^2+(-15x)/21x^2+13=0

We multiply all the terms by the denominator


7x^2+(-15x)+13*21x^2=0

Wy multiply elements

7x^2+273x^2+(-15x)=0

We get rid of parentheses

7x^2+273x^2-15x=0

We add all the numbers together, and all the variables

280x^2-15x=0

a = 280; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·280·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*280}=\frac{0}{560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*280}=\frac{30}{560}
=3/56
$