14n^2-39n+33=-2n-2+8n^2

Solution for 14n^2-39n+33=-2n-2+8n^2 equation:

14n^2-39n+33=-2n-2+8n^2

We move all terms to the left:

14n^2-39n+33-(-2n-2+8n^2)=0

We get rid of parentheses

14n^2-8n^2+2n-39n+2+33=0

We add all the numbers together, and all the variables

6n^2-37n+35=0

a = 6; b = -37; c = +35;
Δ = b2-4ac
Δ = -372-4·6·35
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-23}{2*6}=\frac{14}{12}
=1+1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+23}{2*6}=\frac{60}{12}
=5
$