7n^2-2=448

Solution for 7n^2-2=448 equation:

7n^2-2=448

We move all terms to the left:

7n^2-2-(448)=0

We add all the numbers together, and all the variables

7n^2-450=0

a = 7; b = 0; c = -450;
Δ = b2-4ac
Δ = 02-4·7·(-450)
Δ = 12600
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:

$\sqrt{\Delta}=\sqrt{12600}=\sqrt{900*14}=\sqrt{900}*\sqrt{14}=30\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{14}}{2*7}=\frac{0-30\sqrt{14}}{14}
=-\frac{30\sqrt{14}}{14}
=-\frac{15\sqrt{14}}{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{14}}{2*7}=\frac{0+30\sqrt{14}}{14}
=\frac{30\sqrt{14}}{14}
=\frac{15\sqrt{14}}{7}
$