5x 2 +3=8x+7

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

1. First, let's rearrange the equation to bring all terms to one side. This gives us: 5x^2 - 8x + 3 - 7 = 0.

2. Simplifying this, we get: 5x^2 - 8x - 4 = 0.

3. Now, we can solve this quadratic equation using the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a). Here, a = 5, b = -8, and c = -4.

4. Plugging these values into the formula, we get: x = [8 ± sqrt((-8)^2 - 45(-4))] / (2*5).

5. Simplifying under the square root, we get: x = [8 ± sqrt(64 + 80)] / 10.

6. Further simplifying, we get: x = [8 ± sqrt(144)] / 10.

7. Taking the square root of 144, we get: x = [8 ± 12] / 10.

8. This gives us two solutions: x = 20/10 = 2 and x = -4/10 = -0.4.

So, the solutions to the equation 5x^2 + 3 = 8x + 7 are x = 2 and x = -0.4.