w+1/w=4

Solution for w+1/w=4 equation:

w+1/w=4

We move all terms to the left:

w+1/w-(4)=0


Domain of the equation: w!=0

w∈R


We multiply all the terms by the denominator


w*w-4*w+1=0

We add all the numbers together, and all the variables

-4w+w*w+1=0

Wy multiply elements

w^2-4w+1=0

a = 1; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·1·1
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{3}}{2*1}=\frac{4-2\sqrt{3}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{3}}{2*1}=\frac{4+2\sqrt{3}}{2}
$