2x=1/4x+4

Solution for 2x=1/4x+4 equation:

2x=1/4x+4

We move all terms to the left:

2x-(1/4x+4)=0


Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

2x-1/4x-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-16x-1=0

a = 8; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·8·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*8}=\frac{16-12\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*8}=\frac{16+12\sqrt{2}}{16}
$