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x+2.5x+1/3x=16.5
We move all terms to the left:
x+2.5x+1/3x-(16.5)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
3.5x+1/3x-16.5=0
We multiply all the terms by the denominator
(3.5x)*3x-(16.5)*3x+1=0
We add all the numbers together, and all the variables
(+3.5x)*3x-(16.5)*3x+1=0
We multiply parentheses
9x^2-49.5x+1=0
a = 9; b = -49.5; c = +1;
Δ = b2-4ac
Δ = -49.52-4·9·1
Δ = 2414.25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49.5)-\sqrt{2414.25}}{2*9}=\frac{49.5-\sqrt{2414.25}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49.5)+\sqrt{2414.25}}{2*9}=\frac{49.5+\sqrt{2414.25}}{18} $
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