w+4=32/w

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Solution for w+4=32/w equation:



w+4=32/w
We move all terms to the left:
w+4-(32/w)=0
Domain of the equation: w)!=0
w!=0/1
w!=0
w∈R
We add all the numbers together, and all the variables
w-(+32/w)+4=0
We get rid of parentheses
w-32/w+4=0
We multiply all the terms by the denominator
w*w+4*w-32=0
We add all the numbers together, and all the variables
4w+w*w-32=0
Wy multiply elements
w^2+4w-32=0
a = 1; b = 4; c = -32;
Δ = b2-4ac
Δ = 42-4·1·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*1}=\frac{-16}{2} =-8 $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*1}=\frac{8}{2} =4 $

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