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7/2x+5/3x=11/6
We move all terms to the left:
7/2x+5/3x-(11/6)=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!=0/3
x!=0
x∈R
7/2x+5/3x-(+11/6)=0
We get rid of parentheses
7/2x+5/3x-11/6=0
We calculate fractions
(-198x^2)/216x^2+756x/216x^2+360x/216x^2=0
We multiply all the terms by the denominator
(-198x^2)+756x+360x=0
We add all the numbers together, and all the variables
(-198x^2)+1116x=0
We get rid of parentheses
-198x^2+1116x=0
a = -198; b = 1116; c = 0;
Δ = b2-4ac
Δ = 11162-4·(-198)·0
Δ = 1245456
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{1245456}=1116$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1116)-1116}{2*-198}=\frac{-2232}{-396} =5+7/11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1116)+1116}{2*-198}=\frac{0}{-396} =0 $
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