180=110+x+1/3x

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Solution for 180=110+x+1/3x equation:



180=110+x+1/3x
We move all terms to the left:
180-(110+x+1/3x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-(x+1/3x+110)+180=0
We get rid of parentheses
-x-1/3x-110+180=0
We multiply all the terms by the denominator
-x*3x-110*3x+180*3x-1=0
Wy multiply elements
-3x^2-330x+540x-1=0
We add all the numbers together, and all the variables
-3x^2+210x-1=0
a = -3; b = 210; c = -1;
Δ = b2-4ac
Δ = 2102-4·(-3)·(-1)
Δ = 44088
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:
$\sqrt{\Delta}=\sqrt{44088}=\sqrt{4*11022}=\sqrt{4}*\sqrt{11022}=2\sqrt{11022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-2\sqrt{11022}}{2*-3}=\frac{-210-2\sqrt{11022}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+2\sqrt{11022}}{2*-3}=\frac{-210+2\sqrt{11022}}{-6} $

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