Solve the given equation for the indicated variable. Assume that all denominator are nonze...

Solve the given equation for the indicated variable. Assume that all denominator are nonzero and that all variables represent positive real number. (See Example 1.)

Example 1

Solve v = mx2 + x. (Assume that m and v are positive.)

Solution

The equation is quadratic in x become of the x2 term. Before we use the quadratic formula, we write the equation in standard form:

Let a = m, b = 1, and c = −v. Then the quadratic formula gives