State the value of the discriminate. Then determine the number of real roots of the equation.

n (7n+8) = -10

no real solutions

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 : a ≠ 0

Then the nature of the roots can be determined from the discriminant

b² - 4ac

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then no real roots

Given

n (7n + 8) = - 10 ← distribute left side

7n² + 8n = - 10 (add 10 to both sides)

7n² + 8n + 10 = 0 ← in standard form

with a = 7, b = 8 and c = 10, thus

b² - 4ac = 8² - (4 * 7 * 10) = 64 - 280 = - 216

Since b² - 4ac < 0 the equation has no real roots