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5/6x-1/3=12-2/5x
We move all terms to the left:
5/6x-1/3-(12-2/5x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/6x-(-2/5x+12)-1/3=0
We get rid of parentheses
5/6x+2/5x-12-1/3=0
We calculate fractions
(-150x^2)/270x^2+225x/270x^2+108x/270x^2-12=0
We multiply all the terms by the denominator
(-150x^2)+225x+108x-12*270x^2=0
We add all the numbers together, and all the variables
(-150x^2)+333x-12*270x^2=0
Wy multiply elements
(-150x^2)-3240x^2+333x=0
We get rid of parentheses
-150x^2-3240x^2+333x=0
We add all the numbers together, and all the variables
-3390x^2+333x=0
a = -3390; b = 333; c = 0;
Δ = b2-4ac
Δ = 3332-4·(-3390)·0
Δ = 110889
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{110889}=333$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(333)-333}{2*-3390}=\frac{-666}{-6780} =111/1130 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(333)+333}{2*-3390}=\frac{0}{-6780} =0 $
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