How do you solve #7x^2+5x+8=0# using the quadratic formula?

Employ the following new quadratic formula in graphic form (Socratic Search): y = 7x^2 + 5x + 8 = 0 D = d^2 = b^2 - 4ac = 25 - 224 = - 199 < 0 Real roots do not exist because D < 0.

To solve the quadratic equation (7x^2 + 5x + 8 = 0) using the quadratic formula, first identify the coefficients (a), (b), and (c):

(a = 7), (b = 5), (c = 8)

Then, plug these values into the quadratic formula:

(x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}})

Substitute (a), (b), and (c) into the formula:

(x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 7 \cdot 8}}}}{{2 \cdot 7}})

Calculate the discriminant under the square root:

(b^2 - 4ac = 5^2 - 4 \cdot 7 \cdot 8 = 25 - 224 = -199)

Since the discriminant is negative ((-199)), there are no real solutions. The solutions are complex.

Therefore, the solutions for (x) are:

(x = \frac{{-5 + \sqrt{{-199}}}}{{14}}) and (x = \frac{{-5 - \sqrt{{-199}}}}{{14}})