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2/3x+2(x+7)=17
We move all terms to the left:
2/3x+2(x+7)-(17)=0
Domain of the equation: 3x!=0We multiply parentheses
x!=0/3
x!=0
x∈R
2/3x+2x+14-17=0
We multiply all the terms by the denominator
2x*3x+14*3x-17*3x+2=0
Wy multiply elements
6x^2+42x-51x+2=0
We add all the numbers together, and all the variables
6x^2-9x+2=0
a = 6; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·6·2
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{-(-9)-\sqrt{33}}{2*6}=\frac{9-\sqrt{33}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*6}=\frac{9+\sqrt{33}}{12} $
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