$\mathbb{L}=\left\{{\displaystyle \frac{2}{3}}\right\}\backslash mathbb\{L\}=\backslash left\backslash \{\backslash dfrac\{2\}\{3\}\backslash right\backslash \}$

Die allgemeine Form einer quadratischen Gleichung lautet:

$a{x}^2+bx+c=0\backslash hspace\{40mm\}\; ax^2+bx+c=0$

Die Mitternachtsformel lautet:

$x_{\mathrm{1,2}}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-b\pm \sqrt{b^2-4ac}}{2a}}\backslash hspace\{40mm\}x\_\{1\{,\}2\}=\backslash dfrac\{-b\backslash pm\backslash sqrt\{D\}\}\{2a\}=\backslash dfrac\{-b\backslash pm\backslash sqrt\{b^2-4ac\}\}\{2a\}$

$2x^2-5x-3=0\backslash hspace\{40mm\}\; 2x^2-5x-3=0$

Setze die Zahlenwerte entsprechend in die Mitternachtsformel ein.

$x_{\mathrm{1,2}}={\displaystyle \frac{5\pm \sqrt{25-4\cdot 2\cdot (-3)}}{4}}\backslash hspace\{40mm\}\; x\_\{1\{,\}2\}=\backslash dfrac\{5\backslash pm\backslash sqrt\{25-4\backslash cdot\; 2\backslash cdot(-3)\}\}\{4\}$

$x_{\mathrm{1,2}}={\displaystyle \frac{5\pm \sqrt{25+24}}{4}}\backslash hspace\{40mm\}\; x\_\{1\{,\}2\}=\backslash dfrac\{5\backslash pm\backslash sqrt\{25+24\}\}\{4\}$

$x_{\mathrm{1,2}}={\displaystyle \frac{5\pm 7}{4}}\backslash hspace\{40mm\}\; x\_\{1\{,\}2\}=\backslash dfrac\{5\backslash pm7\}\{4\}$

$\Rightarrow x_1=3\text{ und }{x}_2=-{\displaystyle \frac{1}{2}}\backslash hspace\{32mm\}\backslash Rightarrow\; x\_\{1\}=3\backslash \; \backslash text\{und\}\backslash \; x\_\{2\}=-\backslash dfrac\{1\}\{2\}$

$\mathbb{L}=\{3;-{\displaystyle \frac{1}{2}}\}\backslash mathbb\{L\}=\backslash left\backslash \{3;-\backslash dfrac\{1\}\{2\}\backslash right\backslash \}$