Final answer:
To solve the quadratic equations, we bring each equation to standard form and apply the quadratic formula with corresponding coefficients to find the roots.
Step-by-step explanation:
To solve the quadratic equation 3x(x + 6) = -10, we first need to bring the equation to the standard form, which is ax^2 + bx + c = 0. We can do this by distributing the 3x across the parentheses and then adding 10 to both sides to get the following equation: 3x^2 + 18x + 10 = 0.
In this case, the coefficients are a = 3, b = 18, and c = 10. We then apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a). Substituting these values into the formula gives us the roots of the equation.
Similarly, to solve the quadratic equation t^2 + 10t - 2000 = 0, we recognize that it is already in standard form. Using the quadratic formula with the coefficients a = 1, b = 10, and c = -2000 gives us the solutions for t.