$x^2+x-42$ = 0

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

x_1,2 = $-\frac{1}{2}$ ± $\sqrt{\frac{169}{4}}$

x₁ = $-\frac{1}{2}$ - $\frac{13}{2}$ = $-\frac{14}{2}$ = -7

x₂ = $-\frac{1}{2}$ + $\frac{13}{2}$ = $\frac{12}{2}$ = 6

L = { $-7$; $6$}

$-7x-8$ = $-x^2$ | - ( $-x^2$)

$-7x-8+x^2$ = 0

sortieren

$x^2-7x-8$ = 0

D = ${\left(-\frac{7}{2}\right)}^2-\left(-8\right)$ = $\frac{49}{4}$$+$ $8$ = $\frac{49}{4}$$+$ $\frac{32}{4}$ = $\frac{81}{4}$

x_1,2 = $\frac{7}{2}$ ± $\sqrt{\frac{81}{4}}$

x₁ = $\frac{7}{2}$ - $\frac{9}{2}$ = $-\frac{2}{2}$ = -1

x₂ = $\frac{7}{2}$ + $\frac{9}{2}$ = $\frac{16}{2}$ = 8

L = { $-1$; $8$}