$$150+90t-\frac{451}{100}t^2 = 0$$
Answer
$$ \begin{matrix}t_1 = \dfrac{ 4500 }{ 451 }-\dfrac{ 50 \sqrt{ 10806}}{ 451 } & t_2 = \dfrac{ 4500 }{ 451 }+\dfrac{ 50 \sqrt{ 10806}}{ 451 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 150+90t-\frac{451}{100}t^2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100\cdot150+100\cdot90t-100 \cdot \frac{451}{100}t^2 &= 100\cdot0&& \text{cancel out the denominators} \\[1 em]15000+9000t-451t^2 &= 0&& \text{simplify left side} \\[1 em]-451t^2+9000t+15000 &= 0&& \\[1 em] \end{aligned} $$
$ -451x^{2}+9000x+15000 = 0 $ is a quadratic equation.
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