k^2=9/16

Solution for k^2=9/16 equation:

k^2=9/16

We move all terms to the left:

k^2-(9/16)=0

We add all the numbers together, and all the variables

k^2-(+9/16)=0

We get rid of parentheses

k^2-9/16=0

We multiply all the terms by the denominator


k^2*16-9=0

Wy multiply elements

16k^2-9=0

a = 16; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·16·(-9)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*16}=\frac{-24}{32}
=-3/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*16}=\frac{24}{32}
=3/4
$