solve for x:3x^2-4x=15

To solve the equation 3x^2 - 4x = 15, we need to rearrange it into the standard quadratic equation form: ax^2 + bx + c = 0.

Step 1: Move all the terms to one side of the equation:
3x^2 - 4x - 15 = 0

Step 2: Now we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 3, b = -4, and c = -15. To solve this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Step 3: Plug in the values of a, b, and c into the quadratic formula and simplify:

x = (4 ± √((-4)^2 - 4 * 3 * (-15))) / (2 * 3)
= (4 ± √(16 + 180)) / 6
= (4 ± √196) / 6
= (4 ± 14) / 6

Step 4: Simplify further:

For the plus sign:
x = (4 + 14) / 6
= 18/6
= 3

For the minus sign:
x = (4 - 14) / 6
= -10/6
= -5/3

So the solutions to the equation 3x^2 - 4x = 15 are x = 3 and x = -5/3.