#### Answer

$n=2.56,-1.96$

#### Work Step by Step

$5n^2-3n-15=10$
Rewrite the equation as:
$n^2-\frac{3}{5}n-3=2$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-\frac{3}{5}$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-\frac{3}{5})^2}{4}=\dfrac{9}{100}$
To complete the square, add $\dfrac{9}{100}$ on both sides.
$n^2-\frac{3}{5}n-3+\dfrac{9}{100}=2+\dfrac{9}{100}$
$\implies (n-\dfrac{3}{10})^2=\dfrac{509}{100}$
$\implies (n-\dfrac{3}{10})=2.26$
and
$\implies (n-\dfrac{3}{10})=-2.26$
or, $n=2.56,-1.96$