2w-11/2w=16

Solution for 2w-11/2w=16 equation:

2w-11/2w=16

We move all terms to the left:

2w-11/2w-(16)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We multiply all the terms by the denominator


2w*2w-16*2w-11=0

Wy multiply elements

4w^2-32w-11=0

a = 4; b = -32; c = -11;
Δ = b2-4ac
Δ = -322-4·4·(-11)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-20\sqrt{3}}{2*4}=\frac{32-20\sqrt{3}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+20\sqrt{3}}{2*4}=\frac{32+20\sqrt{3}}{8}
$