2n^2-6n-18=16

Solution for 2n^2-6n-18=16 equation:

2n^2-6n-18=16

We move all terms to the left:

2n^2-6n-18-(16)=0

We add all the numbers together, and all the variables

2n^2-6n-34=0

a = 2; b = -6; c = -34;
Δ = b2-4ac
Δ = -62-4·2·(-34)
Δ = 308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{77}}{2*2}=\frac{6-2\sqrt{77}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{77}}{2*2}=\frac{6+2\sqrt{77}}{4}
$