$x^2-7x-18$ = 0

D = ${\left(-\frac{7}{2}\right)}^2-\left(-18\right)$ = $\frac{49}{4}$$+$ $18$ = $\frac{49}{4}$$+$ $\frac{72}{4}$ = $\frac{121}{4}$

x_1,2 = $\frac{7}{2}$ ± $\sqrt{\frac{121}{4}}$

x₁ = $\frac{7}{2}$ - $\frac{11}{2}$ = $-\frac{4}{2}$ = -2

x₂ = $\frac{7}{2}$ + $\frac{11}{2}$ = $\frac{18}{2}$ = 9

L = { $-2$; $9$}

$42-13x$ = $-x^2$ | - ( $-x^2$)

$42-13x+x^2$ = 0

sortieren

$x^2-13x+42$ = 0

D = ${\left(-\frac{13}{2}\right)}^2-42$ = $\frac{169}{4}$ $-$ $42$ = $\frac{169}{4}$$-$ $\frac{168}{4}$ = $\frac{1}{4}$

x_1,2 = $\frac{13}{2}$ ± $\sqrt{\frac{1}{4}}$

x₁ = $\frac{13}{2}$ - $\frac{1}{2}$ = $\frac{12}{2}$ = 6

x₂ = $\frac{13}{2}$ + $\frac{1}{2}$ = $\frac{14}{2}$ = 7

L = { $6$; $7$}