# Exercise ID366

Algebra → Quadratic equations, inequalities and systems of equations → Quadratic inequalities
[Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 9] [Number of characters: 123]

Solve the following inequality on the set of real numbers!

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${x}^{2}-x-2=0\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$${x}_{1,2}=\frac{-\left(-1\right)±\sqrt{{\left(-1\right)}^{2}-4·1·\left(-2\right)}}{2·1}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$${x}_{1,2}=\frac{1±\sqrt{1+8}}{2}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$${x}_{1,2}=\frac{1±\sqrt{9}}{2}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$${x}_{1,2}=\frac{1±3}{2}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$
$x\in \left[-1,2\right]$

${x}_{1,2}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a};a{x}^{2}+bx+c=0$