1/4x+x=18

Solution for 1/4x+x=18 equation:

1/4x+x=18

We move all terms to the left:

1/4x+x-(18)=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-18=0

We multiply all the terms by the denominator


x*4x-18*4x+1=0

Wy multiply elements

4x^2-72x+1=0

a = 4; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·4·1
Δ = 5168
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:

$\sqrt{\Delta}=\sqrt{5168}=\sqrt{16*323}=\sqrt{16}*\sqrt{323}=4\sqrt{323}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{323}}{2*4}=\frac{72-4\sqrt{323}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{323}}{2*4}=\frac{72+4\sqrt{323}}{8}
$