Answer: [tex]x = 2, -\frac{10}{3}[/tex]
Write the equation in standard form: [tex]ax^{2} + bx + c = 0[/tex].
[tex]8x(x - 2) - 20 = 5x(x - 4)\\\\8x^{2} - 16x - 20 = 5x^{2} - 20x\\\\3x^{2} - 16x - 20 = -20x\\\\3x^{2} + 4x -20 = 0[/tex]
Use the quadratic formula. (+-) = ±
[tex]\frac{-b (+-) \sqrt{b^{2} - 4ac } }{2a}[/tex]
Substitute in the values, where a = 3, b = 4, and c = -20, and simplify.
[tex]\frac{-4(+-)\sqrt{(4)^{2} - 4(3)(-20)} }{2(3)} \\\\\frac{-4(+-)\sqrt{16 + 240} }{6}} \\\\\frac{-4(+-)\sqrt{256} }{6} \\\\\frac{-4(+-)16}{6} \\\\\frac{-4 + 16}{6}, \frac{-4 - 16}{6} \\\\\frac{12}{6}, \frac{-20}{6} \\\\2, -\frac{10}{3}[/tex]
[tex]x = 2, -\frac{10}{3}[/tex]
