3n^2+9=138

Solution for 3n^2+9=138 equation:

3n^2+9=138

We move all terms to the left:

3n^2+9-(138)=0

We add all the numbers together, and all the variables

3n^2-129=0

a = 3; b = 0; c = -129;
Δ = b2-4ac
Δ = 02-4·3·(-129)
Δ = 1548
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:

$\sqrt{\Delta}=\sqrt{1548}=\sqrt{36*43}=\sqrt{36}*\sqrt{43}=6\sqrt{43}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{43}}{2*3}=\frac{0-6\sqrt{43}}{6}
=-\frac{6\sqrt{43}}{6}
=-\sqrt{43}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{43}}{2*3}=\frac{0+6\sqrt{43}}{6}
=\frac{6\sqrt{43}}{6}
=\sqrt{43}
$