4n^2-9=180

Solution for 4n^2-9=180 equation:

4n^2-9=180

We move all terms to the left:

4n^2-9-(180)=0

We add all the numbers together, and all the variables

4n^2-189=0

a = 4; b = 0; c = -189;
Δ = b2-4ac
Δ = 02-4·4·(-189)
Δ = 3024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{21}}{2*4}=\frac{0-12\sqrt{21}}{8}
=-\frac{12\sqrt{21}}{8}
=-\frac{3\sqrt{21}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{21}}{2*4}=\frac{0+12\sqrt{21}}{8}
=\frac{12\sqrt{21}}{8}
=\frac{3\sqrt{21}}{2}
$