Question

the solution set of 3x^2-11+4=0

Answer 1

I assume you forgot to write the x with the coefficient 11, and you really mean this equation.

3x^2 - 11x + 4 = 0

Use the quadratic with a = 3, b = -11, and c = 4.

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-(-11) \pm \sqrt{(-11)^2 - 4(3)(4)}}{2(3)}$

$x = \dfrac{11 \pm \sqrt{121 - 48}}{6}$

$x = \dfrac{11 \pm \sqrt{73}}{6}$

$x = \dfrac{11}{6} + \dfrac{\sqrt{73}}{6} ~or~ x = \dfrac{11}{6} - \dfrac{\sqrt{73}}{6}$