81n2+33=42

Solution for 81n2+33=42 equation:

81n^2+33=42

We move all terms to the left:

81n^2+33-(42)=0

We add all the numbers together, and all the variables

81n^2-9=0

a = 81; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·81·(-9)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*81}=\frac{-54}{162}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*81}=\frac{54}{162}
=1/3
$