2n^2-54=3n

Solution for 2n^2-54=3n equation:

2n^2-54=3n

We move all terms to the left:

2n^2-54-(3n)=0

a = 2; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·2·(-54)
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*2}=\frac{-18}{4}
=-4+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*2}=\frac{24}{4}
=6
$