2n^2=14-1

Solution for 2n^2=14-1 equation:

2n^2=14-1

We move all terms to the left:

2n^2-(14-1)=0

We add all the numbers together, and all the variables

2n^2-13=0

a = 2; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·2·(-13)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*2}=\frac{0-2\sqrt{26}}{4}
=-\frac{2\sqrt{26}}{4}
=-\frac{\sqrt{26}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*2}=\frac{0+2\sqrt{26}}{4}
=\frac{2\sqrt{26}}{4}
=\frac{\sqrt{26}}{2}
$