Question

="0 = - 4.9t {}^{2} + 27t + 2.4" alt="0 = - 4.9t {}^{2} + 27t + 2.4" align="absmiddle" class="latex-formula">

Answer 1

$0 = - 4.9t {}^{2} + 27t + 2.4$
Convert decimals to fractions

$0 = - \frac{49}{10} t {}^{2} + 27t + \frac{12}{5}$
Multiply both sides by 10

$0 = - 49t {}^{2} + 270t + 24$
Move expression to the left.

$0 + 49t {}^{2} - 270t - 24 = 0$
Remove zero.

$49t {}^{2} - 270t - 24 = 0$Solve the quadratic equation.

$t = \frac{ - ( - 270) + - \sqrt{( - 270) {}^{2} - 4 \times 49 \times ( - 24) } }{2 \times 49}$
Remove parenthesis and calculate.

$t = \frac{270 + - \sqrt{72900 + 4704} }{98}$
Add the numbers

$t = \frac{270 + - 77604}{98}$
Separate the solutions

$t = \frac{270 + \sqrt{77604} }{98} \\ t = \frac{270 - \sqrt{77604} }{98}$
The final solution are
$t1 = \frac{270 - \sqrt{77604} }{98} , t2 = \frac{270 + \sqrt{77604} }{98}$