[tex]0 = - 4.9t {}^{2} + 27t + 2.4[/tex]

[tex]0 = - 4.9t {}^{2} + 27t + 2.4[/tex]
Convert decimals to fractions

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

[tex]0 = - 49t {}^{2} + 270t + 24[/tex]
Move expression to the left.

[tex]0 + 49t {}^{2} - 270t - 24 = 0[/tex]
Remove zero.

[tex]49t {}^{2} - 270t - 24 = 0[/tex]Solve the quadratic equation.

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

[tex]t = \frac{270 + - \sqrt{72900 + 4704} }{98} [/tex]
Add the numbers

[tex]t = \frac{270 + - 77604}{98} [/tex]
Separate the solutions

[tex]t = \frac{270 + \sqrt{77604} }{98} \\ t = \frac{270 - \sqrt{77604} }{98} [/tex]
The final solution are
[tex]t1 = \frac{270 - \sqrt{77604} }{98} , t2 = \frac{270 + \sqrt{77604} }{98} [/tex]