Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } - 3 x = 4$
A) $\frac { 3 \pm \sqrt { 41 } } { 4 }$
B) $\frac { 3 \pm \sqrt { 41 } } { 2 }$
C) $\frac { - 3 \pm \sqrt { 41 } } { 2 }$
D) $\frac { - 3 \pm \sqrt { 41 } } { 4 }$
E)no real solutions

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac {-b \pm \sqrt {b^2 - 4ac}} {2a}$. For the equation $2 x ^ { 2 } - 3 x = 4$, $a = 2$, $b = -3$, and $c = -4$. Substituting these values into the quadratic formula gives:$$x = \frac {-(-3) \pm \sqrt {(-3)^2 - 4(2)(-4)}} {2(2)}$$$$= \frac {3 \pm \sqrt {9 + 32}} {4}$$$$= \frac {3 \pm \sqrt {41}} {4}$$Therefore, the real solutions of the equation are $\frac {3 \pm \sqrt {41}} {4}$.

Use the Quadratic Formula to Find All Real Solutions of the Equation