Final answer:
To solve the equation 2n(4n+5)+6=0 using the quadratic formula, we need to rewrite it in standard form. The solutions to the equation are expressed in standard a+bi form.
Step-by-step explanation:
To solve the equation 2n(4n+5)+6=0 using the quadratic formula, we first need to rewrite it in standard form. Distributing 2n across the parentheses gives us 8n² + 10n + 6 = 0. Now we can identify the coefficients: a = 8, b = 10, and c = 6.
Next, we can substitute these values into the quadratic formula: n = (-b ± √(b² - 4ac)) / (2a). Plugging in the values, we get n = (-10 ± √(10² - 4*8*6)) / (2*8). Simplifying further, n = (-10 ± √(100 - 192)) / 16. This simplifies to n = (-10 ± √(-92)) / 16.
Since the square root of a negative number results in a complex number, the solution to this equation is expressed in standard a+bi form. Therefore, the solutions are n = -10/16 + (i√92)/16 and n = -10/16 - (i√92)/16.