X+1/4x=120

Solution for X+1/4x=120 equation:

X+1/4X=120

We move all terms to the left:

X+1/4X-(120)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-120*4X+1=0

Wy multiply elements

4X^2-480X+1=0

a = 4; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·4·1
Δ = 230384
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:

$\sqrt{\Delta}=\sqrt{230384}=\sqrt{1936*119}=\sqrt{1936}*\sqrt{119}=44\sqrt{119}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-44\sqrt{119}}{2*4}=\frac{480-44\sqrt{119}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+44\sqrt{119}}{2*4}=\frac{480+44\sqrt{119}}{8}
$