An astronaut on the moon throws a baseball upward. The astronaut is 6 ft. 6 in. tall, and the initial velocity of the ball is 50 ft. per sec. The height s of the ball in feet is given by the equation s = 2.7t^2 + 50t + 6.5, where t is the number of seconds after the ball was thrown. Complete parts A and B. A: After How many seconds is the ball 20 ft above the moon's surface?

In algebra, a quadratic equation is any equation that can be rearranged in standard form as ax2 + bx + c = 0 , where x represents an unknown, and a, b, and c represent known figures, where a ≠ 0. still, not quadratic,( If a = 0( and b ≠ 0) also the equation is direct.
The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure and the constant or free term.
The values of x that satisfy the equation are called results of the equation, and roots or bottoms of the expression on its left- hand side. A quadratic equation has at most two solutions.
However, one says that it's a double root, If there's only one solution.
A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two.
A quadratic equation can be regard into an original equation.

[tex]h(t) = -2.7t^2 + 30t + 6.5\\\\12 = -2.7t^2 + 30t + 6.5\\\\2.7t^2 - 30t - 6.5 + 12 = 0[/tex]

use the quadratic formula

t = 0.1865 seconds or 10.925 seconds

Thus, After 0.1865 seconds or 10.925 seconds is the ball 20 ft above the moon's surface as determined using quadratic equation.

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