7n^2-127=420

Solution for 7n^2-127=420 equation:

7n^2-127=420

We move all terms to the left:

7n^2-127-(420)=0

We add all the numbers together, and all the variables

7n^2-547=0

a = 7; b = 0; c = -547;
Δ = b2-4ac
Δ = 02-4·7·(-547)
Δ = 15316
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:

$\sqrt{\Delta}=\sqrt{15316}=\sqrt{4*3829}=\sqrt{4}*\sqrt{3829}=2\sqrt{3829}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3829}}{2*7}=\frac{0-2\sqrt{3829}}{14}
=-\frac{2\sqrt{3829}}{14}
=-\frac{\sqrt{3829}}{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3829}}{2*7}=\frac{0+2\sqrt{3829}}{14}
=\frac{2\sqrt{3829}}{14}
=\frac{\sqrt{3829}}{7}
$