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1/3x+x+2x=180
We move all terms to the left:
1/3x+x+2x-(180)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
3x+1/3x-180=0
We multiply all the terms by the denominator
3x*3x-180*3x+1=0
Wy multiply elements
9x^2-540x+1=0
a = 9; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·9·1
Δ = 291564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{291564}=\sqrt{36*8099}=\sqrt{36}*\sqrt{8099}=6\sqrt{8099}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{8099}}{2*9}=\frac{540-6\sqrt{8099}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{8099}}{2*9}=\frac{540+6\sqrt{8099}}{18} $
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