10x 2 −4x+1=6x 2

Sure, let's solve the equation step by step:

1. First, let's rewrite the equation: 10x^2 - 4x + 1 = 6x^2
2. Next, let's move all terms to one side of the equation: 10x^2 - 6x^2 - 4x + 1 = 0
3. This simplifies to: 4x^2 - 4x + 1 = 0
4. Now, let's divide all terms by 4 to simplify further: x^2 - x + 1/4 = 0
5. This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a)
6. In this case, a = 1, b = -1, and c = 1/4. Substituting these values into the quadratic formula gives: x = [1 ± sqrt((-1)^2 - 411/4)] / (2*1)
7. Simplifying under the square root gives: x = [1 ± sqrt(1 - 1)] / 2
8. So, x = [1 ± sqrt(0)] / 2
9. Therefore, the solution to the equation is x = 1/2.