3n^2+42n=-144

Solution for 3n^2+42n=-144 equation:

3n^2+42n=-144

We move all terms to the left:

3n^2+42n-(-144)=0

We add all the numbers together, and all the variables

3n^2+42n+144=0

a = 3; b = 42; c = +144;
Δ = b2-4ac
Δ = 422-4·3·144
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6}{2*3}=\frac{-48}{6}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6}{2*3}=\frac{-36}{6}
=-6
$