section 3.5 homework\n10. solve the equation by graphing.\n6x² + 2x - 3 = -3x² + x - 4.\noptions:\na. x =…

Explanation:

Step1: Rearrange the equation

First, we want to set the equation (6x^{2}+2x - 3=-3x^{2}+x - 4) to the form (ax^{2}+bx + c = 0). Add (3x^{2}-x + 4) to both sides: (6x^{2}+3x^{2}+2x - x-3 + 4=0) Simplify to get (9x^{2}+x + 1 = 0)

Step2: Analyze the quadratic equation

For a quadratic equation (ax^{2}+bx + c = 0) ((a = 9), (b = 1), (c = 1)), the discriminant is given by (\Delta=b^{2}-4ac). Calculate (\Delta=(1)^{2}-4\times9\times1=1 - 36=- 35)

Step3: Determine the nature of solutions

Since (\Delta=-35<0), the quadratic equation (9x^{2}+x + 1 = 0) has no real solutions. This means the graphs of (y = 6x^{2}+2x - 3) and (y=-3x^{2}+x - 4) do not intersect (or have no real intersection points), so the original equation has no real solution.

Answer:

h. no real solution