w^2=9/6

Solution for w^2=9/6 equation:

w^2=9/6

We move all terms to the left:

w^2-(9/6)=0

We add all the numbers together, and all the variables

w^2-(+9/6)=0

We get rid of parentheses

w^2-9/6=0

We multiply all the terms by the denominator


w^2*6-9=0

Wy multiply elements

6w^2-9=0

a = 6; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·6·(-9)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*6}=\frac{0-6\sqrt{6}}{12}
=-\frac{6\sqrt{6}}{12}
=-\frac{\sqrt{6}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*6}=\frac{0+6\sqrt{6}}{12}
=\frac{6\sqrt{6}}{12}
=\frac{\sqrt{6}}{2}
$