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2x+2=2/3x+9
We move all terms to the left:
2x+2-(2/3x+9)=0
Domain of the equation: 3x+9)!=0We get rid of parentheses
x∈R
2x-2/3x-9+2=0
We multiply all the terms by the denominator
2x*3x-9*3x+2*3x-2=0
Wy multiply elements
6x^2-27x+6x-2=0
We add all the numbers together, and all the variables
6x^2-21x-2=0
a = 6; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·6·(-2)
Δ = 489
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{-(-21)-\sqrt{489}}{2*6}=\frac{21-\sqrt{489}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{489}}{2*6}=\frac{21+\sqrt{489}}{12} $
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