How many real-number solutions does the equation have? –7x² + 6x + 3 = 0
To determine the number of real-number solutions for the given quadratic equation -7x² + 6x + 3 = 0, we can use the discriminant formula from the quadratic formula.
The discriminant (Δ) is calculated using the formula: Δ = b² - 4ac, where a, b, and c are the coefficients of x², x, and the constant term, respectively, in the quadratic equation ax² + bx + c = 0.
In this case, a = -7, b = 6, and c = 3. Plugging these values into the discriminant formula, we get:
Δ = (6)² - 4 * (-7) * (3)
Δ = 36 + 84
Δ = 120
Since the discriminant is positive (Δ > 0), this means there are two distinct real-number solutions for the equation -7x² + 6x + 3 = 0.