If t > 0 and (3t)² - 5 (3t) - 14 = 0, what is the value of t?

The correct answer is: 2.33

Hint:-
We simplify the given equation to find the solution.
Step-by-step solution:-
(3t)² - 5 (3t) - 14 = 0
∴ 9t² -15t - 14 = 0
Comparing the above quadratic equation with the general form i.e. ax² + bx + c = 0, we get-
a = 9, b = -15 & c = -14
We can solve the above quadratic equation using factorization method as follows-
Steps for Factorization method-
Step-1: a c = 9 -14 = -126
Step-2: Factorize -126 in such a way that the 2 factors, when added, gives the value b = -15
i.e. -126 = -21 6
& -21 + 6 = -15 = b
∴ 9t² - 21t + 6t - 14 = 0
∴ 3t (3t - 7) + 2 (3t - 7) = 0
∴ (3t + 2) (3t - 7) = 0
∴ either (3t + 2) = 0 or (3t - 7) = 0
∴ either 3t = -2 or 3t = 7
∴ either t = or t =
But it is given in the question that t > 0
∴ t =  is not a valid solution
∴ t =  
Final Answer:-
∴ Value of t for the given conditions is 

Exponentiation is the process of expressing large numbers in terms of powers. In other words, exponent refers to the no. of times a number is multiplied by itself. For example, '6' is multiplied by itself four times, yielding 6 x 6 x 6 x 6 and written as 64. The exponent is '4,' and the base is '6'. This can be read as '6' multiplied by 4.
¶The symbol () represents the exponent. This symbol () is known as a carrot. '4' raised to '2' can, for example, be written as 42 or 42. Thus, 4^2 = 4 × 4 = 16. The table below depicts the representation of a few numerical expressions with exponents.