Rewrite the equation as .

Multiply each term by and simplify.

Multiply each term in by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Apply the distributive property.

Multiply by .

Subtract from both sides of the equation.

Move to the left side of the equation by subtracting it from both sides.

Factor the left side of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Reorder terms.

Replace the left side with the factored expression.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Divide by .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Factor out of .

Factor out of .

Multiply each term in by

Multiply each term in by .

Simplify .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Apply the distributive property.

Simplify.

Multiply .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

Simplify .

The final answer is the combination of both solutions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for t 0.5=(6t)/(t^2+4)