Question

Use the quadratic formula to solve the equation: 8x(x - 2) - 20 = 5x(x - 4)​

Answer 1

Answer: $x = 2, -\frac{10}{3}$

Write the equation in standard form: $ax^{2} + bx + c = 0$.

$8x(x - 2) - 20 = 5x(x - 4)\\\\8x^{2} - 16x - 20 = 5x^{2} - 20x\\\\3x^{2} - 16x - 20 = -20x\\\\3x^{2} + 4x -20 = 0$

Use the quadratic formula. (+-) = ±

$\frac{-b (+-) \sqrt{b^{2} - 4ac } }{2a}$

Substitute in the values, where a = 3, b = 4, and c = -20, and simplify.

$\frac{-4(+-)\sqrt{(4)^{2} - 4(3)(-20)} }{2(3)} \\\\\frac{-4(+-)\sqrt{16 + 240} }{6}} \\\\\frac{-4(+-)\sqrt{256} }{6} \\\\\frac{-4(+-)16}{6} \\\\\frac{-4 + 16}{6}, \frac{-4 - 16}{6} \\\\\frac{12}{6}, \frac{-20}{6} \\\\2, -\frac{10}{3}$

$x = 2, -\frac{10}{3}$