w^2=35/100

Solution for w^2=35/100 equation:

w^2=35/100

We move all terms to the left:

w^2-(35/100)=0

We add all the numbers together, and all the variables

w^2-(+35/100)=0

We get rid of parentheses

w^2-35/100=0

We multiply all the terms by the denominator


w^2*100-35=0

Wy multiply elements

100w^2-35=0

a = 100; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·100·(-35)
Δ = 14000
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:

$\sqrt{\Delta}=\sqrt{14000}=\sqrt{400*35}=\sqrt{400}*\sqrt{35}=20\sqrt{35}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{35}}{2*100}=\frac{0-20\sqrt{35}}{200}
=-\frac{20\sqrt{35}}{200}
=-\frac{\sqrt{35}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{35}}{2*100}=\frac{0+20\sqrt{35}}{200}
=\frac{20\sqrt{35}}{200}
=\frac{\sqrt{35}}{10}
$