Use the discriminant to determine the number and type of solutions to the quadratic equation. Show all work for full credit! 2 + 8 = 13

The equation has two different real solutions

Step-by-step explanation:

The discriminant of the quadratic equation ax² + bx + c = 0 is Δ = b² - 4ac, it used to find the number and type of solutions

Δ > 0, means two different real solutions Δ = 0, means one real solution Δ < 0, means no real solutions

∵ The equation is a² + 8a = 13

- Put it in the form ax² + bx + c = 0

- Subtract 13 from both sides

∴ a² + 8a - 13 = 0

∴ The coefficient of a² = 1, the coefficient of a = 8 and the

numerical term = - 13

∵ Δ = (coefficient of a) ² - 4 (coefficient of a²) (numerical term)

∴ Δ = (8) ² - 4 (1) (-13)

∴ Δ = 64 + 52

∴ Δ = 116

∵ Δ > 0

∴ The equation has two different real solutions