x+1/4x+x-54=180

Solution for x+1/4x+x-54=180 equation:

x+1/4x+x-54=180

We move all terms to the left:

x+1/4x+x-54-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/4x-234=0

We multiply all the terms by the denominator


2x*4x-234*4x+1=0

Wy multiply elements

8x^2-936x+1=0

a = 8; b = -936; c = +1;
Δ = b2-4ac
Δ = -9362-4·8·1
Δ = 876064
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:

$\sqrt{\Delta}=\sqrt{876064}=\sqrt{16*54754}=\sqrt{16}*\sqrt{54754}=4\sqrt{54754}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-936)-4\sqrt{54754}}{2*8}=\frac{936-4\sqrt{54754}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-936)+4\sqrt{54754}}{2*8}=\frac{936+4\sqrt{54754}}{16}
$