30n^2-144=-42

Solution for 30n^2-144=-42 equation:

30n^2-144=-42

We move all terms to the left:

30n^2-144-(-42)=0

We add all the numbers together, and all the variables

30n^2-102=0

a = 30; b = 0; c = -102;
Δ = b2-4ac
Δ = 02-4·30·(-102)
Δ = 12240
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:

$\sqrt{\Delta}=\sqrt{12240}=\sqrt{144*85}=\sqrt{144}*\sqrt{85}=12\sqrt{85}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{85}}{2*30}=\frac{0-12\sqrt{85}}{60}
=-\frac{12\sqrt{85}}{60}
=-\frac{\sqrt{85}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{85}}{2*30}=\frac{0+12\sqrt{85}}{60}
=\frac{12\sqrt{85}}{60}
=\frac{\sqrt{85}}{5}
$