Question

$6x^2 + 11x = -3$

Explanation:

Step1: Rearrange to standard quadratic form

$6x^2 + 11x + 3 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=6$, $b=11$, $c=3$

Step3: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Substitute values:
$$x=\frac{-11\pm\sqrt{11^2-4\times6\times3}}{2\times6}$$

Step4: Calculate discriminant

$\sqrt{121-72}=\sqrt{49}=7$

Step5: Solve for x

$x=\frac{-11+7}{12}=\frac{-4}{12}=-\frac{1}{3}$ and $x=\frac{-11-7}{12}=\frac{-18}{12}=-\frac{3}{2}$

Answer:

$x=-\frac{1}{3}$ or $x=-\frac{3}{2}$