3n^2-n=102n

Solution for 3n^2-n=102n equation:

3n^2-n=102n

We move all terms to the left:

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

We add all the numbers together, and all the variables

3n^2-103n=0

a = 3; b = -103; c = 0;
Δ = b2-4ac
Δ = -1032-4·3·0
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-103)-103}{2*3}=\frac{0}{6}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-103)+103}{2*3}=\frac{206}{6}
=34+1/3
$