4/7x-1/3x=5

Solution for 4/7x-1/3x=5 equation:

4/7x-1/3x=5

We move all terms to the left:

4/7x-1/3x-(5)=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+(-7x)/21x^2-5=0

We multiply all the terms by the denominator


12x+(-7x)-5*21x^2=0

Wy multiply elements

-105x^2+12x+(-7x)=0

We get rid of parentheses

-105x^2+12x-7x=0

We add all the numbers together, and all the variables

-105x^2+5x=0

a = -105; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-105)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-105}=\frac{-10}{-210}
=1/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-105}=\frac{0}{-210}
=0
$