4x+1/4x=4576

Solution for 4x+1/4x=4576 equation:

4x+1/4x=4576

We move all terms to the left:

4x+1/4x-(4576)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


4x*4x-4576*4x+1=0

Wy multiply elements

16x^2-18304x+1=0

a = 16; b = -18304; c = +1;
Δ = b2-4ac
Δ = -183042-4·16·1
Δ = 335036352
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:

$\sqrt{\Delta}=\sqrt{335036352}=\sqrt{64*5234943}=\sqrt{64}*\sqrt{5234943}=8\sqrt{5234943}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18304)-8\sqrt{5234943}}{2*16}=\frac{18304-8\sqrt{5234943}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18304)+8\sqrt{5234943}}{2*16}=\frac{18304+8\sqrt{5234943}}{32}
$