7/3x-1/3=-1/5x+4

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

7/3x-1/3=-1/5x+4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

7/3x+1/5x-4-1/3=0

We calculate fractions


35x/135x^2+27x/135x^2+(-5x)/135x^2-4=0

We multiply all the terms by the denominator


35x+27x+(-5x)-4*135x^2=0

We add all the numbers together, and all the variables

62x+(-5x)-4*135x^2=0

Wy multiply elements

-540x^2+62x+(-5x)=0

We get rid of parentheses

-540x^2+62x-5x=0

We add all the numbers together, and all the variables

-540x^2+57x=0

a = -540; b = 57; c = 0;
Δ = b2-4ac
Δ = 572-4·(-540)·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-57}{2*-540}=\frac{-114}{-1080}
=19/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+57}{2*-540}=\frac{0}{-1080}
=0
$