solve the equation using the quadratic for\n\n3x² = 8x + 9\n\nthe solution set is {}.\n(simplify your…

Explanation:

Step1: Transform to standard quadratic form

$$3x^{2}-8x - 9=0$$ For a quadratic equation (ax^{2}+bx + c = 0), here (a = 3), (b=-8), (c=-9).

Step2: Use the quadratic formula (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a})

First, calculate the discriminant (\Delta=b^{2}-4ac). Substitute (a = 3), (b=-8), (c=-9) into (\Delta): (\Delta=(-8)^{2}-4\times3\times(-9)=64 + 108=172) Then (x=\frac{-(-8)\pm\sqrt{172}}{2\times3}=\frac{8\pm2\sqrt{43}}{6}=\frac{4\pm\sqrt{43}}{3})

Answer:

(\left{\frac{4 + \sqrt{43}}{3},\frac{4-\sqrt{43}}{3}\right})