\( a = -5, b = 40 \) → \( t = -\frac{40}{2(-5)} = \frac{40}{10} = 4 \)

["Understanding the Equation: How to Calculate ( t ) from ( a = -5 ) and ( b = 40 )", "When solving equations involving variables, precise substitution and algebraic manipulation are key. Take the example where ( a = -5 ) and ( b = 40 ), and you want to find ( t ) in the expression:", "[\nt = -\frac{b}{2a}\n]", "This formula often appears in contexts such as calculating time, rate, or statistical measures, especially those involving quadratic relationships.", "### Substituting the Known Values", "Given ( a = -5 ) and ( b = 40 ), substitute these values into the equation:", "[\nt = -\frac{40}{2(-5)}\n]", "Now simplify the denominator:", "[\n2(-5) = -10\n]", "So the expression becomes:", "[\nt = -\frac{40}{-10}\n]", "### Simplifying the Fraction", "Negative signs cancel out in the numerator and denominator:", "[\nt = \frac{40}{10} = 4\n]", "### Final Result", "Thus,\n[\nt = 4\n]", "### Why This Formula Matters", "This computation is a simple yet powerful illustration of linear relationships derived from more complex equations—common in algebra, physics, and data analysis. Understanding how constants ( a ) and ( b ) influence the final value of ( t ) helps clarify dependencies and supports accurate problem-solving.", "### Summary", "- Substitute ( a = -5 ), ( b = 40 ) into ( t = -\frac{b}{2a} )\n- Simplify denominator: ( 2a = -10 )\n- Evaluate fraction: ( t = -\frac{40}{-10} = 4 )", "This clear, step-by-step approach reinforces algebraic fluency and supports confident solving of similar equations.", "---", "Keywords for SEO:\na = -5, b = 40, t = -40/(2a), calculation example, algebra problem solved, simplified equation, linear equation result, mathematical steps, values substitution, t value calculation\nMeta Description:\nLearn how to compute ( t = -\frac{40}{2(-5)} ) step-by-step. Get a clear, correct solution with simplified algebra showing ( t = 4 ). Ideal for algebra students and problem-solvers."]