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3x+5=1/3x+5
We move all terms to the left:
3x+5-(1/3x+5)=0
Domain of the equation: 3x+5)!=0We get rid of parentheses
x∈R
3x-1/3x-5+5=0
We multiply all the terms by the denominator
3x*3x-5*3x+5*3x-1=0
Wy multiply elements
9x^2-15x+15x-1=0
We add all the numbers together, and all the variables
9x^2-1=0
a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18} =-1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18} =1/3 $
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