24=w2-9

Solution for 24=w2-9 equation:

24=w2-9

We move all terms to the left:

24-(w2-9)=0

We add all the numbers together, and all the variables

-(+w^2-9)+24=0

We get rid of parentheses

-w^2+9+24=0

We add all the numbers together, and all the variables

-1w^2+33=0

a = -1; b = 0; c = +33;
Δ = b2-4ac
Δ = 02-4·(-1)·33
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{33}}{2*-1}=\frac{0-2\sqrt{33}}{-2}
=-\frac{2\sqrt{33}}{-2}
=-\frac{\sqrt{33}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{33}}{2*-1}=\frac{0+2\sqrt{33}}{-2}
=\frac{2\sqrt{33}}{-2}
=\frac{\sqrt{33}}{-1}
$