(2/5x)-(1/3x)=4

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Solution for (2/5x)-(1/3x)=4 equation:



(2/5x)-(1/3x)=4
We move all terms to the left:
(2/5x)-(1/3x)-(4)=0
Domain of the equation: 5x)!=0
x!=0/1
x!=0
x∈R
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+2/5x)-(+1/3x)-4=0
We get rid of parentheses
2/5x-1/3x-4=0
We calculate fractions
6x/15x^2+(-5x)/15x^2-4=0
We multiply all the terms by the denominator
6x+(-5x)-4*15x^2=0
Wy multiply elements
-60x^2+6x+(-5x)=0
We get rid of parentheses
-60x^2+6x-5x=0
We add all the numbers together, and all the variables
-60x^2+x=0
a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-60}=\frac{-2}{-120} =1/60 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120} =0 $

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