14n^2-5=33n

Solution for 14n^2-5=33n equation:

14n^2-5=33n

We move all terms to the left:

14n^2-5-(33n)=0

a = 14; b = -33; c = -5;
Δ = b2-4ac
Δ = -332-4·14·(-5)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-37}{2*14}=\frac{-4}{28}
=-1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+37}{2*14}=\frac{70}{28}
=2+1/2
$