Final answer:
To solve the equation 3x^2+2x-1=3-4x, we can rearrange it into the form ax^2+bx+c=0 and then use the quadratic formula to find the solutions.
Step-by-step explanation:
To solve the equation 3x^2+2x-1=3-4x, we need to rearrange it so that it is in the form ax^2+bx+c=0. By moving all the terms to one side, we get 3x^2+4x-4=0. This is a quadratic equation, and we can solve it using the quadratic formula.
The quadratic formula is x = (-b ± √(b^2-4ac))/(2a). In this case, a=3, b=4, and c=-4.
Substituting these values into the formula gives us x = (-4 ± √(4^2-4(3)(-4)))/(2(3)).
Simplifying further, we have x = (-4 ± √(16+48))/6, which becomes x = (-4 ± √(64))/6, and finally x = (-4 ± 8)/6.
Therefore, the solutions to the equation are x = (-4+8)/6 = 4/6 = 2/3 and x = (-4-8)/6 = -12/6 = -2.