180=x+1/4x

Solution for 180=x+1/4x equation:

180=x+1/4x

We move all terms to the left:

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

We get rid of parentheses

-x-1/4x+180=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+720x-1=0

a = -4; b = 720; c = -1;
Δ = b2-4ac
Δ = 7202-4·(-4)·(-1)
Δ = 518384
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:

$\sqrt{\Delta}=\sqrt{518384}=\sqrt{16*32399}=\sqrt{16}*\sqrt{32399}=4\sqrt{32399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(720)-4\sqrt{32399}}{2*-4}=\frac{-720-4\sqrt{32399}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(720)+4\sqrt{32399}}{2*-4}=\frac{-720+4\sqrt{32399}}{-8}
$