3n2-n=102

Solution for 3n2-n=102 equation:

3n^2-n=102

We move all terms to the left:

3n^2-n-(102)=0

We add all the numbers together, and all the variables

3n^2-1n-102=0

a = 3; b = -1; c = -102;
Δ = b2-4ac
Δ = -12-4·3·(-102)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-35}{2*3}=\frac{-34}{6}
=-5+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+35}{2*3}=\frac{36}{6}
=6
$