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1/9x-10=21/3x+6
We move all terms to the left:
1/9x-10-(21/3x+6)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 3x+6)!=0We get rid of parentheses
x∈R
1/9x-21/3x-6-10=0
We calculate fractions
3x/27x^2+(-189x)/27x^2-6-10=0
We add all the numbers together, and all the variables
3x/27x^2+(-189x)/27x^2-16=0
We multiply all the terms by the denominator
3x+(-189x)-16*27x^2=0
Wy multiply elements
-432x^2+3x+(-189x)=0
We get rid of parentheses
-432x^2+3x-189x=0
We add all the numbers together, and all the variables
-432x^2-186x=0
a = -432; b = -186; c = 0;
Δ = b2-4ac
Δ = -1862-4·(-432)·0
Δ = 34596
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{34596}=186$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-186}{2*-432}=\frac{0}{-864} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+186}{2*-432}=\frac{372}{-864} =-31/72 $
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