n*n+6=374

Solution for n*n+6=374 equation:

n*n+6=374

We move all terms to the left:

n*n+6-(374)=0

We add all the numbers together, and all the variables

n*n-368=0

Wy multiply elements

n^2-368=0

a = 1; b = 0; c = -368;
Δ = b2-4ac
Δ = 02-4·1·(-368)
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{23}}{2*1}=\frac{0-8\sqrt{23}}{2}
=-\frac{8\sqrt{23}}{2}
=-4\sqrt{23}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{23}}{2*1}=\frac{0+8\sqrt{23}}{2}
=\frac{8\sqrt{23}}{2}
=4\sqrt{23}
$