4/7x-2/3x=13

Solution for 4/7x-2/3x=13 equation:

4/7x-2/3x=13

We move all terms to the left:

4/7x-2/3x-(13)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


12x/21x^2+(-14x)/21x^2-13=0

We multiply all the terms by the denominator


12x+(-14x)-13*21x^2=0

Wy multiply elements

-273x^2+12x+(-14x)=0

We get rid of parentheses

-273x^2+12x-14x=0

We add all the numbers together, and all the variables

-273x^2-2x=0

a = -273; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-273)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-273}=\frac{0}{-546}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-273}=\frac{4}{-546}
=-2/273
$