# Solve for t d=vt+1/2*(at^2) Rewrite the equation as .
Multiply .
Combine and .
Combine and .
Move to the left side of the equation by subtracting it from both sides.
Multiply through by the least common denominator , then simplify.
Apply the distributive property.
Simplify.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Move .
Reorder and .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Let . Substitute for all occurrences of .
Apply the product rule to .
Raise to the power of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Replace all occurrences of with .
Simplify each term.
Rewrite using the commutative property of multiplication.
Multiply by .
Rewrite as .
Pull terms out from under the radical.
Simplify .
The final answer is the combination of both solutions.
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