### Quadratic equations

Solution based on the antique arabic method

\(x,p,q>0\)

- \(x^{2}+px=q\) (Al-Khwarizmi)
- \(x^{2}+px=q\) (another version) (Al-Khwarizmi)
- \(x^{2}+q=px(x<\frac{p}{2})\) (Al-Khwarizmi)
- \(x^{2}+q=px(x>\frac{p}{2})\) (Al-Hamid Ibn Turk)
- \(px+q=x^{2}\) (Al-Khwarizmi)

**Note:** The apps only find the **positive** solutions of the indicated equations, since the unknown \(x\) is considered as the length of a line segment. The equation \(x^{2}+q=px\) has only two positive solutions if and only if \(p^{2}>4q\). The positive solution of the equation \(px+q=x^{2}\) is always greater than \(p\).