Question

solve the equation by the method of your choice
(4x + 3)(x + 2) = 3

the solution set is
(simplify your answer. type an exact answer, using radicals and i as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)

Explanation:

Step1: Expand left-hand side

$(4x+3)(x+2) = 4x^2 + 8x + 3x + 6 = 4x^2 + 11x + 6$

Step2: Rearrange to standard quadratic form

$4x^2 + 11x + 6 - 3 = 0$
$4x^2 + 11x + 3 = 0$

Step3: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=4$, $b=11$, $c=3$.
$x=\frac{-11\pm\sqrt{11^2-4(4)(3)}}{2(4)}$

Step4: Calculate discriminant and simplify

$\sqrt{121-48}=\sqrt{73}$
$x=\frac{-11\pm\sqrt{73}}{8}$

Answer:

$\frac{-11+\sqrt{73}}{8}, \frac{-11-\sqrt{73}}{8}$