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5/6x+21=-2/3x-18
We move all terms to the left:
5/6x+21-(-2/3x-18)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x-18)!=0We get rid of parentheses
x∈R
5/6x+2/3x+18+21=0
We calculate fractions
15x/18x^2+12x/18x^2+18+21=0
We add all the numbers together, and all the variables
15x/18x^2+12x/18x^2+39=0
We multiply all the terms by the denominator
15x+12x+39*18x^2=0
We add all the numbers together, and all the variables
27x+39*18x^2=0
Wy multiply elements
702x^2+27x=0
a = 702; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·702·0
Δ = 729
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{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*702}=\frac{-54}{1404} =-1/26 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*702}=\frac{0}{1404} =0 $
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