Question

`0 = - 4.9t {}^(2) + 27t + 2.4`

Answer 1

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


`0 = - (49)/(10) t {}^(2) + 27t + (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 * 49 * ( - 24) } }{2 * 49}`
Remove parenthesis and calculate.


`t = (270 + - √(72900 + 4704) )/(98)`
Add the numbers


`t = (270 + - 77604)/(98)`
Separate the solutions


`t = (270 + √(77604) )/(98) \\ t = (270 - √(77604) )/(98)`
The final solution are

`t1 = (270 - √(77604) )/(98) , t2 = (270 + √(77604) )/(98)`