w-17=-11+16/w

Solution for w-17=-11+16/w equation:

w-17=-11+16/w

We move all terms to the left:

w-17-(-11+16/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-(16/w-11)-17=0

We get rid of parentheses

w-16/w+11-17=0

We multiply all the terms by the denominator


w*w+11*w-17*w-16=0

We add all the numbers together, and all the variables

-6w+w*w-16=0

Wy multiply elements

w^2-6w-16=0

a = 1; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*1}=\frac{-4}{2}
=-2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*1}=\frac{16}{2}
=8
$