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1/3x+x-93+x=180
We move all terms to the left:
1/3x+x-93+x-(180)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
2x+1/3x-273=0
We multiply all the terms by the denominator
2x*3x-273*3x+1=0
Wy multiply elements
6x^2-819x+1=0
a = 6; b = -819; c = +1;
Δ = b2-4ac
Δ = -8192-4·6·1
Δ = 670737
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{-(-819)-\sqrt{670737}}{2*6}=\frac{819-\sqrt{670737}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-819)+\sqrt{670737}}{2*6}=\frac{819+\sqrt{670737}}{12} $
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