Answer:
t = 6 or t = 4/7.
Explanation:
Let's begin by simplifying both sides of the equation:
7(t•2+5t−9)+t = t(7•t−2)+13
First, let's distribute the 7 to the terms inside the parentheses:
14t + 35t - 63 + t = t(7t - 2) + 13
Combine like terms on the left side of the equation:
50t - 63 = 7t^2 - 2t + 13
Next, let's move all the terms to one side of the equation:
7t^2 - 52t + 76 = 0
Now we can use the quadratic formula to solve for t:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 7, b = -52, and c = 76.
Plugging in these values, we get:
t = (52 ± sqrt(52^2 - 4(7)(76))) / (2(7))
t = (52 ± sqrt(1024)) / 14
t = (52 ± 32) / 14
Therefore, the solutions to the equation are:t = 6 or t = 4/7.