1/3x+1/5x=2

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Solution for 1/3x+1/5x=2 equation:



1/3x+1/5x=2
We move all terms to the left:
1/3x+1/5x-(2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We calculate fractions
5x/15x^2+3x/15x^2-2=0
We multiply all the terms by the denominator
5x+3x-2*15x^2=0
We add all the numbers together, and all the variables
8x-2*15x^2=0
Wy multiply elements
-30x^2+8x=0
a = -30; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-30)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-30}=\frac{-16}{-60} =4/15 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-30}=\frac{0}{-60} =0 $

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