x+1/4x=45

Solution for x+1/4x=45 equation:

x+1/4x=45

We move all terms to the left:

x+1/4x-(45)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-45*4x+1=0

Wy multiply elements

4x^2-180x+1=0

a = 4; b = -180; c = +1;
Δ = b2-4ac
Δ = -1802-4·4·1
Δ = 32384
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:

$\sqrt{\Delta}=\sqrt{32384}=\sqrt{64*506}=\sqrt{64}*\sqrt{506}=8\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-8\sqrt{506}}{2*4}=\frac{180-8\sqrt{506}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+8\sqrt{506}}{2*4}=\frac{180+8\sqrt{506}}{8}
$