12n^2+3=51

Solution for 12n^2+3=51 equation:

12n^2+3=51

We move all terms to the left:

12n^2+3-(51)=0

We add all the numbers together, and all the variables

12n^2-48=0

a = 12; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·12·(-48)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*12}=\frac{-48}{24}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*12}=\frac{48}{24}
=2
$