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2/3x+4=7/6x+7
We move all terms to the left:
2/3x+4-(7/6x+7)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x+7)!=0We get rid of parentheses
x∈R
2/3x-7/6x-7+4=0
We calculate fractions
12x/18x^2+(-21x)/18x^2-7+4=0
We add all the numbers together, and all the variables
12x/18x^2+(-21x)/18x^2-3=0
We multiply all the terms by the denominator
12x+(-21x)-3*18x^2=0
Wy multiply elements
-54x^2+12x+(-21x)=0
We get rid of parentheses
-54x^2+12x-21x=0
We add all the numbers together, and all the variables
-54x^2-9x=0
a = -54; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-54)·0
Δ = 81
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-54}=\frac{0}{-108} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-54}=\frac{18}{-108} =-1/6 $
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