w2=32/100

Solution for w2=32/100 equation:

w2=32/100

We move all terms to the left:

w2-(32/100)=0

We add all the numbers together, and all the variables

w2-(+32/100)=0

We add all the numbers together, and all the variables

w^2-(+32/100)=0

We get rid of parentheses

w^2-32/100=0

We multiply all the terms by the denominator


w^2*100-32=0

Wy multiply elements

100w^2-32=0

a = 100; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·100·(-32)
Δ = 12800
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:

$\sqrt{\Delta}=\sqrt{12800}=\sqrt{6400*2}=\sqrt{6400}*\sqrt{2}=80\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{2}}{2*100}=\frac{0-80\sqrt{2}}{200}
=-\frac{80\sqrt{2}}{200}
=-\frac{2\sqrt{2}}{5}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{2}}{2*100}=\frac{0+80\sqrt{2}}{200}
=\frac{80\sqrt{2}}{200}
=\frac{2\sqrt{2}}{5}
$