Solve the following quadratic by either factoring or using the quadratic formula:
6x2 - 5x = 6
6x^2 -5x -6 = 0
(3x+2)*(2x-3) = 0
Take it from there
To solve the quadratic equation 6x^2 - 5x = 6, we can rearrange it to 6x^2 - 5x - 6 = 0.
To factor this quadratic equation, we can try different combinations of factors of -6 that add up to -5. We have:
(3x + 2)(2x - 3) = 0
Setting each factor equal to zero and solving for x, we get:
3x + 2 = 0 or 2x - 3 = 0
Solving these equations for x, we have:
3x = -2 or 2x = 3
x = -2/3 or x = 3/2
So the solutions to the quadratic equation are x = -2/3 and x = 3/2.
Alternatively, we can use the quadratic formula to solve the quadratic equation. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 6x^2 - 5x - 6 = 0, the coefficients are:
a = 6, b = -5, and c = -6.
Substituting these values into the quadratic formula, we have:
x = (-(-5) ± √((-5)^2 - 4 * 6 * (-6))) / (2 * 6)
Simplifying this, we get:
x = (5 ± √(25 + 144)) / 12
x = (5 ± √(169)) / 12
x = (5 ± 13) / 12
So the solutions to the quadratic equation are x = -2/3 and x = 3/2, which matches the solutions obtained by factoring.