Solve for a n=-h^2+7/a

$n = - h^{2} + \frac{7}{a}$

Rewrite the equation as $- h^{2} + \frac{7}{a} = n$ .

$- h^{2} + \frac{7}{a} = n$

Add $h^{2}$ to both sides of the equation.

$\frac{7}{a} = n + h^{2}$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a, 1, 1$

The LCM of one and any expression is the expression.

$a$

Multiply each term in $\frac{7}{a} = n + h^{2}$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{7}{a} = n + h^{2}$ by $a$ .

$\frac{7}{a} a = n a + h^{2} a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{7}{a} a = n a + h^{2} a$

Rewrite the expression.

$7 = n a + h^{2} a$

Solve the equation.

Rewrite the equation as $n a + h^{2} a = 7$ .

$n a + h^{2} a = 7$

Factor $a$ out of $n a + h^{2} a$ .

Factor $a$ out of $n a$ .

$a n + h^{2} a = 7$

Factor $a$ out of $h^{2} a$ .

$a n + a h^{2} = 7$

Factor $a$ out of $a n + a h^{2}$ .

$a (n + h^{2}) = 7$

Divide each term in $a (n + h^{2}) = 7$ by $n + h^{2}$ and simplify.

Divide each term in $a (n + h^{2}) = 7$ by $n + h^{2}$ .

$\frac{a (n + h^{2})}{n + h^{2}} = \frac{7}{n + h^{2}}$

Simplify the left side.

Cancel the common factor of $n + h^{2}$ .

Cancel the common factor.

$\frac{a (n + h^{2})}{n + h^{2}} = \frac{7}{n + h^{2}}$

Divide $a$ by $1$ .

$a = \frac{7}{n + h^{2}}$