How do you solve 8x2 plus 5x plus 6 equals 0?

Answer 1

Using the formula for the solution of a quadratic equation ax2+bx+c=0:

x = (-b +- sqrt(b2-4ac)) / 2a

(There are two roots, one is found by addition of the square root, the other by subtraction of it).

Which for the given equation 8x2+5x+6=0 means a=8, b=5, c=6, giving:

x = (-5 +- sqrt(52-4x8x6)) / (2x8)

x = (-5 +- sqrt(25-192)) / 16

x = (-5 +- sqrt(-167)) / 16

which has no solution

Unless you know about complex numbers and the use of i = sqrt(-1), in which case, the solutions are:

x = -5/16 + 12.9i and x = -5/16 - 12.9i