$$x^2+x = \frac{143}{4}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 11 }{ 2 } & x_2 = -\dfrac{ 13 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+x &= \frac{143}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x^2+4x &= 4\cdot\frac{143}{4}&& \text{cancel out the denominators} \\[1 em]4x^2+4x &= 143&& \text{move all terms to the left hand side } \\[1 em]4x^2+4x-143 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+4x-143 = 0 $ is a quadratic equation.
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