x-2=168/180x

Solution for x-2=168/180x equation:

x-2=168/180x

We move all terms to the left:

x-2-(168/180x)=0


Domain of the equation: 180x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+168/180x)-2=0

We get rid of parentheses

x-168/180x-2=0

We multiply all the terms by the denominator


x*180x-2*180x-168=0

Wy multiply elements

180x^2-360x-168=0

a = 180; b = -360; c = -168;
Δ = b2-4ac
Δ = -3602-4·180·(-168)
Δ = 250560
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:

$\sqrt{\Delta}=\sqrt{250560}=\sqrt{576*435}=\sqrt{576}*\sqrt{435}=24\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-24\sqrt{435}}{2*180}=\frac{360-24\sqrt{435}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+24\sqrt{435}}{2*180}=\frac{360+24\sqrt{435}}{360}
$