w+16/w=10

Solution for w+16/w=10 equation:

w+16/w=10

We move all terms to the left:

w+16/w-(10)=0


Domain of the equation: w!=0

w∈R


We multiply all the terms by the denominator


w*w-10*w+16=0

We add all the numbers together, and all the variables

-10w+w*w+16=0

Wy multiply elements

w^2-10w+16=0

a = 1; b = -10; c = +16;
Δ = b2-4ac
Δ = -102-4·1·16
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*1}=\frac{4}{2}
=2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*1}=\frac{16}{2}
=8
$