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4/9x-11/18x=-2/3
We move all terms to the left:
4/9x-11/18x-(-2/3)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 18x!=0We get rid of parentheses
x!=0/18
x!=0
x∈R
4/9x-11/18x+2/3=0
We calculate fractions
324x^2/1458x^2+648x/1458x^2+(-891x)/1458x^2=0
We multiply all the terms by the denominator
324x^2+648x+(-891x)=0
We get rid of parentheses
324x^2+648x-891x=0
We add all the numbers together, and all the variables
324x^2-243x=0
a = 324; b = -243; c = 0;
Δ = b2-4ac
Δ = -2432-4·324·0
Δ = 59049
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{59049}=243$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-243)-243}{2*324}=\frac{0}{648} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-243)+243}{2*324}=\frac{486}{648} =3/4 $
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