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5/2x+11/12=2/3x
We move all terms to the left:
5/2x+11/12-(2/3x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/2x-(+2/3x)+11/12=0
We get rid of parentheses
5/2x-2/3x+11/12=0
We calculate fractions
198x^2/72x^2+180x/72x^2+(-48x)/72x^2=0
We multiply all the terms by the denominator
198x^2+180x+(-48x)=0
We get rid of parentheses
198x^2+180x-48x=0
We add all the numbers together, and all the variables
198x^2+132x=0
a = 198; b = 132; c = 0;
Δ = b2-4ac
Δ = 1322-4·198·0
Δ = 17424
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{17424}=132$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-132}{2*198}=\frac{-264}{396} =-2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+132}{2*198}=\frac{0}{396} =0 $
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