3/x=3/5x+4

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Solution for 3/x=3/5x+4 equation:



3/x=3/5x+4
We move all terms to the left:
3/x-(3/5x+4)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 5x+4)!=0
x∈R
We get rid of parentheses
3/x-3/5x-4=0
We calculate fractions
15x/5x^2+(-3x)/5x^2-4=0
We multiply all the terms by the denominator
15x+(-3x)-4*5x^2=0
Wy multiply elements
-20x^2+15x+(-3x)=0
We get rid of parentheses
-20x^2+15x-3x=0
We add all the numbers together, and all the variables
-20x^2+12x=0
a = -20; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-20)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-20}=\frac{-24}{-40} =3/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-20}=\frac{0}{-40} =0 $

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