w2=16/9

Solution for w2=16/9 equation:

w2=16/9

We move all terms to the left:

w2-(16/9)=0

We add all the numbers together, and all the variables

w2-(+16/9)=0

We add all the numbers together, and all the variables

w^2-(+16/9)=0

We get rid of parentheses

w^2-16/9=0

We multiply all the terms by the denominator


w^2*9-16=0

Wy multiply elements

9w^2-16=0

a = 9; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·9·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*9}=\frac{-24}{18}
=-1+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*9}=\frac{24}{18}
=1+1/3
$