Answer:
b=(7-sqrd85/6), b=(7+sqrd85/6)
Step-by-step explanation:
3b^2-7b+3=6
3b^2-7b+3-6=0
3b^2-7b-3=0
a=3, b=-7, c=-3
b=7+-sqrd49+36/6
b=(7-sqrd85/6), b=(7+sqrd85/6)
Answer:
[tex]\displaystyle \frac{7 + \sqrt{85}}{6}[/tex] and [tex]\displaystyle \frac{7 - \sqrt{85}}{6}[/tex].
Step-by-step explanation:
(Replace [tex]b[/tex] with [tex]x[/tex] to avoid confusion with symbols in the quadratic equation.)
Notice that the equation [tex]3\, x^{2} - 7\, x + 3 = 6[/tex] is quadratic with respect to the unknown [tex]x[/tex]. Rewrite the equation in standard form [tex]a\, x^{2} + b\, x + c = 0[/tex] before applying the quadratic equation:
[tex]3\, x^{2} - 7\, x + 3 = 6[/tex].
[tex]3\, x^{2} - 7\, x + 3 - 6 = 0[/tex].
[tex]3\, x^{2} + (- 7)\, x + (-3) = 0[/tex].
Thus, for the quadratic equation, [tex]a = 3[/tex], [tex]b = (-7)[/tex], and [tex]c = (-3)[/tex]. Apply the quadratic equation to find the solutions:
[tex]\begin{aligned}x &= \frac{-\, b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-7) + \sqrt{(-7)^{2} - 4 \times 3 \times (-3)}}{2 \times 3} \\ &= \frac{7 + \sqrt{85}}{6}\end{aligned}[/tex].
[tex]\begin{aligned}x &= \frac{-\, b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-7) - \sqrt{(-7)^{2} - 4 \times 3 \times (-3)}}{2 \times 3} \\ &= \frac{7 - \sqrt{85}}{6}\end{aligned}[/tex].
