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2/9x-1/6=2/3x+11
We move all terms to the left:
2/9x-1/6-(2/3x+11)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 3x+11)!=0We get rid of parentheses
x∈R
2/9x-2/3x-11-1/6=0
We calculate fractions
(-81x^2)/972x^2+216x/972x^2+(-648x)/972x^2-11=0
We multiply all the terms by the denominator
(-81x^2)+216x+(-648x)-11*972x^2=0
Wy multiply elements
(-81x^2)-10692x^2+216x+(-648x)=0
We get rid of parentheses
-81x^2-10692x^2+216x-648x=0
We add all the numbers together, and all the variables
-10773x^2-432x=0
a = -10773; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·(-10773)·0
Δ = 186624
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{186624}=432$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*-10773}=\frac{0}{-21546} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*-10773}=\frac{864}{-21546} =-16/399 $
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