8n2-6=306

Solution for 8n2-6=306 equation:

8n^2-6=306

We move all terms to the left:

8n^2-6-(306)=0

We add all the numbers together, and all the variables

8n^2-312=0

a = 8; b = 0; c = -312;
Δ = b2-4ac
Δ = 02-4·8·(-312)
Δ = 9984
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:

$\sqrt{\Delta}=\sqrt{9984}=\sqrt{256*39}=\sqrt{256}*\sqrt{39}=16\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{39}}{2*8}=\frac{0-16\sqrt{39}}{16}
=-\frac{16\sqrt{39}}{16}
=-\sqrt{39}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{39}}{2*8}=\frac{0+16\sqrt{39}}{16}
=\frac{16\sqrt{39}}{16}
=\sqrt{39}
$