Question
Find roots of polynomial $$ p(x) = 7t^2-\frac{11}{3}t-\frac{2}{3} $$
Answer
The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= \dfrac{ 2 }{ 3 }\\[1 em]t_2 &= -\dfrac{ 1 }{ 7 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} 7t^2-\frac{11}{3}t-\frac{2}{3} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 21t^2-11t-2 & = 0 \end{aligned} $$Step 2:
The solutions of $ 21t^2-11t-2 = 0 $ are: $ t = -\dfrac{ 1 }{ 7 } ~ \text{and} ~ t = \dfrac{ 2 }{ 3 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
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