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6x-4=2/3x-2
We move all terms to the left:
6x-4-(2/3x-2)=0
Domain of the equation: 3x-2)!=0We get rid of parentheses
x∈R
6x-2/3x+2-4=0
We multiply all the terms by the denominator
6x*3x+2*3x-4*3x-2=0
Wy multiply elements
18x^2+6x-12x-2=0
We add all the numbers together, and all the variables
18x^2-6x-2=0
a = 18; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·18·(-2)
Δ = 180
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*18}=\frac{6-6\sqrt{5}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*18}=\frac{6+6\sqrt{5}}{36} $
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