w^2=81/16

Solution for w^2=81/16 equation:

w^2=81/16

We move all terms to the left:

w^2-(81/16)=0

We add all the numbers together, and all the variables

w^2-(+81/16)=0

We get rid of parentheses

w^2-81/16=0

We multiply all the terms by the denominator


w^2*16-81=0

Wy multiply elements

16w^2-81=0

a = 16; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·16·(-81)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*16}=\frac{-72}{32}
=-2+1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*16}=\frac{72}{32}
=2+1/4
$