Question

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

Answer 1

Answer:
`x = 2, -(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)} \\\\(-4(+-)√(16 + 240) )/(6)} \\\\(-4(+-)√(256) )/(6) \\\\(-4(+-)16)/(6) \\\\(-4 + 16)/(6), (-4 - 16)/(6) \\\\(12)/(6), (-20)/(6) \\\\2, -(10)/(3)`

`x = 2, -(10)/(3)`