3/x=5/3x-10

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Solution for 3/x=5/3x-10 equation:



3/x=5/3x-10
We move all terms to the left:
3/x-(5/3x-10)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x-10)!=0
x∈R
We get rid of parentheses
3/x-5/3x+10=0
We calculate fractions
9x/3x^2+(-5x)/3x^2+10=0
We multiply all the terms by the denominator
9x+(-5x)+10*3x^2=0
Wy multiply elements
30x^2+9x+(-5x)=0
We get rid of parentheses
30x^2+9x-5x=0
We add all the numbers together, and all the variables
30x^2+4x=0
a = 30; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·30·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*30}=\frac{-8}{60} =-2/15 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*30}=\frac{0}{60} =0 $

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