165=2/3x+x

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Solution for 165=2/3x+x equation: 



165=2/3x+x

We move all terms to the left:

165-(2/3x+x)=0



Domain of the equation: 3x+x)!=0

x∈R



We add all the numbers together, and all the variables

-(+x+2/3x)+165=0

We get rid of parentheses

-x-2/3x+165=0

We multiply all the terms by the denominator


-x*3x+165*3x-2=0

Wy multiply elements

-3x^2+495x-2=0

a = -3; b = 495; c = -2;
Δ = b2-4ac
Δ = 4952-4·(-3)·(-2)
Δ = 245001
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{-(495)-\sqrt{245001}}{2*-3}=\frac{-495-\sqrt{245001}}{-6}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(495)+\sqrt{245001}}{2*-3}=\frac{-495+\sqrt{245001}}{-6}
$

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