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1/3x-2+1/5x+3=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
1/3x+1/5x+1=0
We calculate fractions
5x/15x^2+3x/15x^2+1=0
We multiply all the terms by the denominator
5x+3x+1*15x^2=0
We add all the numbers together, and all the variables
8x+1*15x^2=0
Wy multiply elements
15x^2+8x=0
a = 15; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·15·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*15}=\frac{-16}{30} =-8/15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*15}=\frac{0}{30} =0 $
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