3n^2=-126-39n

Solution for 3n^2=-126-39n equation:

3n^2=-126-39n

We move all terms to the left:

3n^2-(-126-39n)=0

We add all the numbers together, and all the variables

3n^2-(-39n-126)=0

We get rid of parentheses

3n^2+39n+126=0

a = 3; b = 39; c = +126;
Δ = b2-4ac
Δ = 392-4·3·126
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3}{2*3}=\frac{-42}{6}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3}{2*3}=\frac{-36}{6}
=-6
$