36n^2+9=10

Solution for 36n^2+9=10 equation:

36n^2+9=10

We move all terms to the left:

36n^2+9-(10)=0

We add all the numbers together, and all the variables

36n^2-1=0

a = 36; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·36·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*36}=\frac{-12}{72}
=-1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*36}=\frac{12}{72}
=1/6
$