Решите уравнение: (3x^2-5x)/2-(5x^2-8)/3=0.

\[\frac{3x^{2} - 5x}{2} - \frac{5x^{2} - 8}{3} = 0\ \ \ \ \ \ \ \ | \cdot 6\]

\[3 \bullet \left( 3x^{2} - 5x \right) - 2 \bullet \left( 5x^{2} - 8 \right) =\]

\[= 0\]

\[9x^{2} - 15x - 10x^{2} + 16 = 0\]

\[- x^{2} - 15x + 16 = 0\ \ \ \ \ \ \ \ |\ :( - 1)\]

\[x^{2} + 15x - 16 = 0\]

\[D = 15^{2} - 4 \cdot 1 \cdot ( - 16) =\]

\[= 225 + 64 = 289\]

\[x_{1} = \frac{- 15 + \sqrt{289}}{2} = \frac{- 15 + 17}{2} =\]

\[= \frac{2}{2} = 1\]

\[x_{2} = \frac{- 15 - \sqrt{289}}{2} = \frac{- 15 - 17}{2} =\]

\[= \frac{- 32}{2} = - 16\]

\[Ответ:x = 1;\ x = - 16.\]