Solve: $x ( 3 x - 14 ) = 24$
A) $\left\{ 24 , \frac { 38 } { 3 } \right\}$
B) $\left\{ \frac { 4 } { 3 } , - 6 \right\}$
C) $\left\{ - \frac { 4 } { 3 } , 6 \right\}$
D) $\left\{ - \frac { 4 } { 3 } , - 6 \right\}$

Question

Quizplus · Accepted Answer

We can start by expanding the left side of the equation:
$$3x^2 - 14x = 24$$
$$3x^2 - 14x - 24 = 0$$
Then we can use the quadratic formula:
$$x = \frac{-(-14) \pm \sqrt{(-14)^2 - 4(3)(-24)}}{2(3)}$$
Simplifying gives us:
$$x = \frac{14 \pm \sqrt{400}}{6}$$
Therefore, our solutions are:
$$x = \frac{7 \pm 10}{3}$$
$$x = \frac{17}{3}, -\frac{4}{3}$$
Thus, the best choice is C.

Solve x(3x−14)=24x ( 3 x - 14 ) = 24x(3x−14)=24 A) {24,383}\left\{ 24 , \frac { 38 } { 3 } \right\}{24,338​}

Solve $x ( 3 x - 14 ) = 24$ A) $\left\{ 24 , \frac { 38 } { 3 } \right\}$