1/4x+x+1/4x=54

Solution for 1/4x+x+1/4x=54 equation:

1/4x+x+1/4x=54

We move all terms to the left:

1/4x+x+1/4x-(54)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/4x+1/4x-54=0

We multiply all the terms by the denominator


x*4x-54*4x+1+1=0

We add all the numbers together, and all the variables

x*4x-54*4x+2=0

Wy multiply elements

4x^2-216x+2=0

a = 4; b = -216; c = +2;
Δ = b2-4ac
Δ = -2162-4·4·2
Δ = 46624
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:

$\sqrt{\Delta}=\sqrt{46624}=\sqrt{16*2914}=\sqrt{16}*\sqrt{2914}=4\sqrt{2914}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-4\sqrt{2914}}{2*4}=\frac{216-4\sqrt{2914}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+4\sqrt{2914}}{2*4}=\frac{216+4\sqrt{2914}}{8}
$