180-x=1/3(x)

Solution for 180-x=1/3(x) equation:

180-x=1/3(x)

We move all terms to the left:

180-x-(1/3(x))=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)+180=0

We add all the numbers together, and all the variables

-1x-(+1/3x)+180=0

We get rid of parentheses

-1x-1/3x+180=0

We multiply all the terms by the denominator


-1x*3x+180*3x-1=0

Wy multiply elements

-3x^2+540x-1=0

a = -3; b = 540; c = -1;
Δ = b2-4ac
Δ = 5402-4·(-3)·(-1)
Δ = 291588
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:

$\sqrt{\Delta}=\sqrt{291588}=\sqrt{8836*33}=\sqrt{8836}*\sqrt{33}=94\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-94\sqrt{33}}{2*-3}=\frac{-540-94\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+94\sqrt{33}}{2*-3}=\frac{-540+94\sqrt{33}}{-6}
$