3n^2-3n-34=2

Solution for 3n^2-3n-34=2 equation:

3n^2-3n-34=2

We move all terms to the left:

3n^2-3n-34-(2)=0

We add all the numbers together, and all the variables

3n^2-3n-36=0

a = 3; b = -3; c = -36;
Δ = b2-4ac
Δ = -32-4·3·(-36)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*3}=\frac{-18}{6}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*3}=\frac{24}{6}
=4
$