4x=8-1/4x

Solution for 4x=8-1/4x equation:

4x=8-1/4x

We move all terms to the left:

4x-(8-1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(-1/4x+8)=0

We get rid of parentheses

4x+1/4x-8=0

We multiply all the terms by the denominator


4x*4x-8*4x+1=0

Wy multiply elements

16x^2-32x+1=0

a = 16; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·16·1
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{15}}{2*16}=\frac{32-8\sqrt{15}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{15}}{2*16}=\frac{32+8\sqrt{15}}{32}
$