w-2/w=36

Solution for w-2/w=36 equation:

w-2/w=36

We move all terms to the left:

w-2/w-(36)=0


Domain of the equation: w!=0

w∈R


We multiply all the terms by the denominator


w*w-36*w-2=0

We add all the numbers together, and all the variables

-36w+w*w-2=0

Wy multiply elements

w^2-36w-2=0

a = 1; b = -36; c = -2;
Δ = b2-4ac
Δ = -362-4·1·(-2)
Δ = 1304
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:

$\sqrt{\Delta}=\sqrt{1304}=\sqrt{4*326}=\sqrt{4}*\sqrt{326}=2\sqrt{326}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{326}}{2*1}=\frac{36-2\sqrt{326}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{326}}{2*1}=\frac{36+2\sqrt{326}}{2}
$