6n^2-7=65

Solution for 6n^2-7=65 equation:

6n^2-7=65

We move all terms to the left:

6n^2-7-(65)=0

We add all the numbers together, and all the variables

6n^2-72=0

a = 6; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·6·(-72)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*6}=\frac{0-24\sqrt{3}}{12}
=-\frac{24\sqrt{3}}{12}
=-2\sqrt{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*6}=\frac{0+24\sqrt{3}}{12}
=\frac{24\sqrt{3}}{12}
=2\sqrt{3}
$