20=n^2/2+6

Solution for 20=n^2/2+6 equation:

20=n^2/2+6

We move all terms to the left:

20-(n^2/2+6)=0

We get rid of parentheses

-n^2/2-6+20=0

We multiply all the terms by the denominator


-n^2-6*2+20*2=0

We add all the numbers together, and all the variables

-1n^2+28=0

a = -1; b = 0; c = +28;
Δ = b2-4ac
Δ = 02-4·(-1)·28
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-1}=\frac{0-4\sqrt{7}}{-2}
=-\frac{4\sqrt{7}}{-2}
=-\frac{2\sqrt{7}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-1}=\frac{0+4\sqrt{7}}{-2}
=\frac{4\sqrt{7}}{-2}
=\frac{2\sqrt{7}}{-1}
$