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3x+5=3/3x-1
We move all terms to the left:
3x+5-(3/3x-1)=0
Domain of the equation: 3x-1)!=0We get rid of parentheses
x∈R
3x-3/3x+1+5=0
We multiply all the terms by the denominator
3x*3x+1*3x+5*3x-3=0
Wy multiply elements
9x^2+3x+15x-3=0
We add all the numbers together, and all the variables
9x^2+18x-3=0
a = 9; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·9·(-3)
Δ = 432
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{3}}{2*9}=\frac{-18-12\sqrt{3}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{3}}{2*9}=\frac{-18+12\sqrt{3}}{18} $
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