Vgln. tweede graad

Los op. Vermijd indien mogelijk het gebruik van de discriminant.

\(-\frac{1}{5}x=-\frac{1}{15}x^2+\frac{6}{5}\)

\(-\frac{1}{5}x=-\frac{1}{15}x^2+\frac{6}{5} \\ \Leftrightarrow \frac{1}{15}x^2-\frac{1}{5}x-\frac{6}{5}=0 \\ \Leftrightarrow \color{red}{15.} \left(\frac{1}{15}x^2-\frac{1}{5}x-\frac{6}{5}\right)=0 \color{red}{.15} \\ \Leftrightarrow x^2-3x-18=0 \\\text{We zoeken de oplossingen van } \color{blue}{x^2-3x-18=0} \\ \\\begin{align} D & = b^2 - 4.a.c & & \\ & = (-3)^2-4.1.(-18) & &\\ & = 9+72 & & \\ & = 81 & & \\ \\ x_1 & = \frac{-b-\sqrt{D}}{2.a} & x_2 & = \frac{-b+\sqrt{D}}{2.a} \\ & = \frac{-(-3)-\sqrt81}{2.1} & & = \frac{-(-3)+\sqrt81}{2.1} \\ & = \frac{-6}{2} & & = \frac{12}{2} \\ & = -3 & & = 6 \\ \\ V &= \Big\{ -3 ; 6 \Big\} & &\end{align} \\ -----------------\)