7n^2-24=0

Solution for 7n^2-24=0 equation:

7n^2-24=0

a = 7; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·7·(-24)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*7}=\frac{0-4\sqrt{42}}{14}
=-\frac{4\sqrt{42}}{14}
=-\frac{2\sqrt{42}}{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*7}=\frac{0+4\sqrt{42}}{14}
=\frac{4\sqrt{42}}{14}
=\frac{2\sqrt{42}}{7}
$