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2/3x-4+1=x-2
We move all terms to the left:
2/3x-4+1-(x-2)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
2/3x-(x-2)-3=0
We get rid of parentheses
2/3x-x+2-3=0
We multiply all the terms by the denominator
-x*3x+2*3x-3*3x+2=0
Wy multiply elements
-3x^2+6x-9x+2=0
We add all the numbers together, and all the variables
-3x^2-3x+2=0
a = -3; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-3)·2
Δ = 33
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{33}}{2*-3}=\frac{3-\sqrt{33}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*-3}=\frac{3+\sqrt{33}}{-6} $
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