Solve the equation by the quadratic formula. Give only real number solutions.

2x2−3x=−6

1 answer

To solve the equation 2x^2 - 3x = -6 using the quadratic formula, we first need to rewrite the equation in the form ax^2 + bx + c = 0.

The given equation is already in this form, with a = 2, b = -3, and c = -6.

The quadratic formula is given by x = (-b ± √(b^2 - 4ac))/(2a).

Substituting the values of a, b, and c into the formula, we have:

x = (-(-3) ± √((-3)^2 - 4(2)(-6)))/(2(2))
x = (3 ± √(9 + 48))/4
x = (3 ± √57)/4

Therefore, the solutions to the equation 2x^2 - 3x = -6 are x = (3 + √57)/4 and x = (3 - √57)/4.