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2/3x=2+2x
We move all terms to the left:
2/3x-(2+2x)=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-(2x+2)=0
We get rid of parentheses
2/3x-2x-2=0
We multiply all the terms by the denominator
-2x*3x-2*3x+2=0
Wy multiply elements
-6x^2-6x+2=0
a = -6; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-6)·2
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-6}=\frac{6-2\sqrt{21}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-6}=\frac{6+2\sqrt{21}}{-12} $
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