Question
$$\frac{5}{4}t^2+8t-40 = 0$$
Answer
$$ \begin{matrix}t_1 = -\dfrac{ 16 }{ 5 }-\dfrac{ 4 \sqrt{ 66}}{ 5 } & t_2 = -\dfrac{ 16 }{ 5 }+\dfrac{ 4 \sqrt{ 66}}{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{5}{4}t^2+8t-40 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{5}{4}t^2+4\cdot8t-4\cdot40 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]5t^2+32t-160 &= 0&& \\[1 em] \end{aligned} $$
$ 5x^{2}+32x-160 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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