Vgln. tweede graad

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

\(\frac{13}{30}x=-\frac{1}{5}x^2-\frac{1}{5}\)

\(\frac{13}{30}x=-\frac{1}{5}x^2-\frac{1}{5} \\ \Leftrightarrow \frac{1}{5}x^2+\frac{13}{30}x+\frac{1}{5}=0 \\ \Leftrightarrow \color{red}{30.} \left(\frac{1}{5}x^2+\frac{13}{30}x+\frac{1}{5}\right)=0 \color{red}{.30} \\ \Leftrightarrow 6x^2+13x+6=0 \\\text{We zoeken de oplossingen van } \color{blue}{6x^2+13x+6=0} \\ \\\begin{align} D & = b^2 - 4.a.c & & \\ & = (13)^2-4.6.6 & &\\ & = 169-144 & & \\ & = 25 & & \\ \\ x_1 & = \frac{-b-\sqrt{D}}{2.a} & x_2 & = \frac{-b+\sqrt{D}}{2.a} \\ & = \frac{-13-\sqrt25}{2.6} & & = \frac{-13+\sqrt25}{2.6} \\ & = \frac{-18}{12} & & = \frac{-8}{12} \\ & = \frac{-3}{2} & & = \frac{-2}{3} \\ \\ V &= \Big\{ \frac{-3}{2} ; \frac{-2}{3} \Big\} & &\end{align} \\ -----------------\)