How do I solve by using the Quadratic Formula
6x^2 - 7x = - 4
Just plug in your numbers!
6x^2 - 7x + 4 = 0
x = (-b±√(b^2-4ac))/2a = (7±√(49-96))/12
Thanks!
To solve the given quadratic equation using the Quadratic Formula, which is a formula used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, follow these steps:
1. Start with the given equation: 6x^2 - 7x = -4 and rewrite it so that it is in the standard form, ax^2 + bx + c = 0. In this case, add 4 to both sides of the equation to move the constant term to the right side:
6x^2 - 7x + 4 = 0
2. Identify the values of a, b, and c from the quadratic equation: a = 6, b = -7, c = 4.
3. Apply the Quadratic Formula, which is as follows:
x = (-b ± √(b^2 - 4ac)) / (2a)
4. Substitute the values of a, b, and c into the formula:
x = (-(-7) ± √((-7)^2 - 4(6)(4))) / (2(6))
5. Simplify the expression inside the square root:
x = (7 ± √(49 - 96)) / 12
x = (7 ± √(-47)) / 12
6. Since we have a negative value under the square root, the equation has no real solutions. This means that the quadratic equation 6x^2 - 7x = -4 has no real solutions.
In summary, by applying the Quadratic Formula, we determined that the given quadratic equation has no real solutions.