Find the real solutions, if any, of the equation. Use the quadratic formula.
-$3 x ^ { 2 } + x - 7 = 0$
A) $\left\{ \frac { 1 - \sqrt { 85 } } { 6 } , \frac { 1 + \sqrt { 85 } } { 6 } \right\}$
B) no real solution
C) $\left\{ \frac { - 1 - \sqrt { 85 } } { 6 } , \frac { - 1 + \sqrt { 85 } } { 6 } \right\}$
D) $\left\{ \frac { - 1 - \sqrt { 85 } } { 2 } , \frac { - 1 + \sqrt { 85 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For $3x^2 + x - 7 = 0$, $a = 3$, $b = 1$, $c = -7$. The discriminant $b^2 - 4ac = 1 + 84 = 85$, which is positive, indicating two real solutions: $\frac{-1 \pm \sqrt{85}}{6}$.

Find the Real Solutions, If Any, of the Equation 3x2+x−7=03 x ^ { 2 } + x - 7 = 03x2+x−7=0

Find the Real Solutions, If Any, of the Equation $3 x ^ { 2 } + x - 7 = 0$