Question

which are solutions of the equation $4x^2 - 7x = 3x + 24$? choose two correct answers.
$x = 4$
$x = -\frac{3}{4}$
$x = \frac{2}{3}$
$x = 2$
$x = -4$
$x = -3$

Explanation:

Step1: Rearrange to standard quadratic form

$4x^2 - 7x - 3x - 24 = 0$
$4x^2 - 10x - 24 = 0$
Divide all terms by 2: $2x^2 - 5x - 12 = 0$

Step2: Factor the quadratic equation

Find two numbers that multiply to $2\times(-12)=-24$ and add to $-5$: $-8$ and $3$.
Rewrite and factor:
$2x^2 - 8x + 3x - 12 = 0$
$2x(x-4) + 3(x-4) = 0$
$(2x+3)(x-4)=0$

Step3: Solve for x

Set each factor equal to 0:
$x-4=0 \implies x=4$
$2x+3=0 \implies x=-\frac{3}{2}$

Answer:

$x = 4$, $x = -\frac{3}{2}$