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2/3x+1/2x=5/6
We move all terms to the left:
2/3x+1/2x-(5/6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
2/3x+1/2x-(+5/6)=0
We get rid of parentheses
2/3x+1/2x-5/6=0
We calculate fractions
(-60x^2)/216x^2+144x/216x^2+108x/216x^2=0
We multiply all the terms by the denominator
(-60x^2)+144x+108x=0
We add all the numbers together, and all the variables
(-60x^2)+252x=0
We get rid of parentheses
-60x^2+252x=0
a = -60; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-60)·0
Δ = 63504
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{63504}=252$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-60}=\frac{-504}{-120} =4+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-60}=\frac{0}{-120} =0 $
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