2n2+5=121

Solution for 2n2+5=121 equation:

2n^2+5=121

We move all terms to the left:

2n^2+5-(121)=0

We add all the numbers together, and all the variables

2n^2-116=0

a = 2; b = 0; c = -116;
Δ = b2-4ac
Δ = 02-4·2·(-116)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{58}}{2*2}=\frac{0-4\sqrt{58}}{4}
=-\frac{4\sqrt{58}}{4}
=-\sqrt{58}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{58}}{2*2}=\frac{0+4\sqrt{58}}{4}
=\frac{4\sqrt{58}}{4}
=\sqrt{58}
$