x+1/4x=13

Solution for x+1/4x=13 equation:

x+1/4x=13

We move all terms to the left:

x+1/4x-(13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-13*4x+1=0

Wy multiply elements

4x^2-52x+1=0

a = 4; b = -52; c = +1;
Δ = b2-4ac
Δ = -522-4·4·1
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-8\sqrt{42}}{2*4}=\frac{52-8\sqrt{42}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+8\sqrt{42}}{2*4}=\frac{52+8\sqrt{42}}{8}
$