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2x+1=1/3x+5
We move all terms to the left:
2x+1-(1/3x+5)=0
Domain of the equation: 3x+5)!=0We get rid of parentheses
x∈R
2x-1/3x-5+1=0
We multiply all the terms by the denominator
2x*3x-5*3x+1*3x-1=0
Wy multiply elements
6x^2-15x+3x-1=0
We add all the numbers together, and all the variables
6x^2-12x-1=0
a = 6; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·6·(-1)
Δ = 168
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{42}}{2*6}=\frac{12-2\sqrt{42}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{42}}{2*6}=\frac{12+2\sqrt{42}}{12} $
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