8n^2+1=2433

Solution for 8n^2+1=2433 equation:

8n^2+1=2433

We move all terms to the left:

8n^2+1-(2433)=0

We add all the numbers together, and all the variables

8n^2-2432=0

a = 8; b = 0; c = -2432;
Δ = b2-4ac
Δ = 02-4·8·(-2432)
Δ = 77824
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:

$\sqrt{\Delta}=\sqrt{77824}=\sqrt{4096*19}=\sqrt{4096}*\sqrt{19}=64\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{19}}{2*8}=\frac{0-64\sqrt{19}}{16}
=-\frac{64\sqrt{19}}{16}
=-4\sqrt{19}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{19}}{2*8}=\frac{0+64\sqrt{19}}{16}
=\frac{64\sqrt{19}}{16}
=4\sqrt{19}
$