use the quadratic formula to solve for x.\n$6x^2 + 4x - 3 = 0$\n(if there is more than one solution…

Explanation:

Step1: Identify coefficients

For (6x^2 + 4x - 3 = 0), (a = 6), (b = 4), (c = -3).

Step2: Apply quadratic formula

Quadratic formula: (x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}).
Substitute values: (x=\frac{-4\pm\sqrt{4^2 - 4(6)(-3)}}{2(6)}).
Simplify discriminant: (4^2 - 4(6)(-3)=16 + 72 = 88).
So (x=\frac{-4\pm\sqrt{88}}{12}).
Simplify (\sqrt{88}=\sqrt{4\times22}=2\sqrt{22}), so (x=\frac{-4\pm2\sqrt{22}}{12}=\frac{-2\pm\sqrt{22}}{6}).

Answer:

(\frac{-2 + \sqrt{22}}{6},\frac{-2 - \sqrt{22}}{6})