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2/3x+5=2/6x+14
We move all terms to the left:
2/3x+5-(2/6x+14)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x+14)!=0We get rid of parentheses
x∈R
2/3x-2/6x-14+5=0
We calculate fractions
12x/18x^2+(-6x)/18x^2-14+5=0
We add all the numbers together, and all the variables
12x/18x^2+(-6x)/18x^2-9=0
We multiply all the terms by the denominator
12x+(-6x)-9*18x^2=0
Wy multiply elements
-162x^2+12x+(-6x)=0
We get rid of parentheses
-162x^2+12x-6x=0
We add all the numbers together, and all the variables
-162x^2+6x=0
a = -162; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-162)·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-162}=\frac{-12}{-324} =1/27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-162}=\frac{0}{-324} =0 $
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