Solve the equation. $\frac { x ^ { 2 } } { 6 } - \frac { 8 x } { 7 } = - \frac { 6 } { 7 }$
A) $x = 7 ; x = - \frac { 7 } { 6 }$
B) $x = - 7 ; x = - \frac { 6 } { 7 }$
C) $x = - 6 ; x = - \frac { 6 } { 7 }$
D) $x = 6 ; x = \frac { 6 } { 7 }$
E) $x = - 6 ; x = \frac { 7 } { 6 }$

Question

Quizplus · Accepted Answer

First, we need to multiply both sides of the equation by the common denominator, which is 42. This gives us:

$$7x^2 - 48x = -36$$

Next, we bring all the terms to one side:

$$7x^2 - 48x + 36 = 0$$

Finally, we can solve for x using the quadratic formula:

$$x = \frac{-(-48) \pm \sqrt{(-48)^2 - 4(7)(36)}}{2(7)}$$

Simplifying:

$$x = \frac{48 \pm \sqrt{2304 - 1008}}{14}$$

$$x = \frac{48 \pm 36}{14}$$

Which gives us:

$$x = \frac{6}{7} 	ext{ or } x= 6$$

Therefore, the answer is D as it includes both solutions.

Solve the Equation x26−8x7=−67\frac { x ^ { 2 } } { 6 } - \frac { 8 x } { 7 } = - \frac { 6 } { 7 }6x2​−78x​=−76​

Solve the Equation $\frac { x ^ { 2 } } { 6 } - \frac { 8 x } { 7 } = - \frac { 6 } { 7 }$