Solve for a B/a+f^2=5g

$\frac{B}{a} + f^{2} = 5 g$

Step 1

Subtract $f^{2}$ from both sides of the equation.

$\frac{B}{a} = 5 g - f^{2}$

Step 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.

$a$

Step 3

Multiply each term in $\frac{B}{a} = 5 g - f^{2}$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{B}{a} = 5 g - f^{2}$ by $a$ .

$\frac{B}{a} a = 5 g a - f^{2} a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{B}{a} a = 5 g a - f^{2} a$

Rewrite the expression.

$B = 5 g a - f^{2} a$

Step 4

Solve the equation.

Rewrite the equation as $5 g a - f^{2} a = B$ .

$5 g a - f^{2} a = B$

Factor $a$ out of $5 g a - f^{2} a$ .

Factor $a$ out of $5 g a$ .

$a (5 g) - f^{2} a = B$

Factor $a$ out of $- f^{2} a$ .

$a (5 g) + a (- f^{2}) = B$

Factor $a$ out of $a (5 g) + a (- f^{2})$ .

$a (5 g - f^{2}) = B$

Divide each term in $a (5 g - f^{2}) = B$ by $5 g - f^{2}$ and simplify.

Divide each term in $a (5 g - f^{2}) = B$ by $5 g - f^{2}$ .

$\frac{a (5 g - f^{2})}{5 g - f^{2}} = \frac{B}{5 g - f^{2}}$

Simplify the left side.

Cancel the common factor of $5 g - f^{2}$ .

Cancel the common factor.

$\frac{a (5 g - f^{2})}{5 g - f^{2}} = \frac{B}{5 g - f^{2}}$

Divide $a$ by $1$ .

$a = \frac{B}{5 g - f^{2}}$