180-x=x+(1/4x)

Solution for 180-x=x+(1/4x) equation:

180-x=x+(1/4x)

We move all terms to the left:

180-x-(x+(1/4x))=0


Domain of the equation: 4x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(x+(+1/4x))+180=0

We add all the numbers together, and all the variables

-1x-(x+(+1/4x))+180=0

We multiply all the terms by the denominator


-1x*4x))-(x+(+180*4x))+1=0

Wy multiply elements

-4x^2+720x=0

a = -4; b = 720; c = 0;
Δ = b2-4ac
Δ = 7202-4·(-4)·0
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(720)-720}{2*-4}=\frac{-1440}{-8}
=+180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(720)+720}{2*-4}=\frac{0}{-8}
=0
$