x+1/4x=180

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

x+1/4x=180

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


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}
$