180/(k^2)=45

Solution for 180/(k^2)=45 equation:

180/(k^2)=45

We move all terms to the left:

180/(k^2)-(45)=0


Domain of the equation: k^2!=0

k^2!=0/

k^2!=√0

k!=0

k∈R


We multiply all the terms by the denominator


-45*k^2+180=0

We add all the numbers together, and all the variables

-45k^2+180=0

a = -45; b = 0; c = +180;
Δ = b2-4ac
Δ = 02-4·(-45)·180
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-180}{2*-45}=\frac{-180}{-90}
=+2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+180}{2*-45}=\frac{180}{-90}
=-2
$