2n^2-14=3n

Solution for 2n^2-14=3n equation:

2n^2-14=3n

We move all terms to the left:

2n^2-14-(3n)=0

a = 2; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·2·(-14)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*2}=\frac{-8}{4}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*2}=\frac{14}{4}
=3+1/2
$