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3x=2/3x=
We move all terms to the left:
3x-(2/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3x-(+2/3x)=0
We get rid of parentheses
3x-2/3x=0
We multiply all the terms by the denominator
3x*3x-2=0
Wy multiply elements
9x^2-2=0
a = 9; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·9·(-2)
Δ = 72
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*9}=\frac{0-6\sqrt{2}}{18} =-\frac{6\sqrt{2}}{18} =-\frac{\sqrt{2}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*9}=\frac{0+6\sqrt{2}}{18} =\frac{6\sqrt{2}}{18} =\frac{\sqrt{2}}{3} $
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