30n^2-144=-42n

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

30n^2-144=-42n

We move all terms to the left:

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

We get rid of parentheses

30n^2+42n-144=0

a = 30; b = 42; c = -144;
Δ = b2-4ac
Δ = 422-4·30·(-144)
Δ = 19044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19044}=138$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-138}{2*30}=\frac{-180}{60}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+138}{2*30}=\frac{96}{60}
=1+3/5
$