How do you solve $3 m^{2} - 7 m = 3$ $3m^2 - 7m = 3$ using the quadratic formula?

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How do you solve $3 m^{2} - 7 m = 3$ $3m^2 - 7m = 3$ using the quadratic formula?

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Answer 1 · 2016-04-26T13:42:15

$\frac{7 + \sqrt{85}}{6}$ $(7 + sqrt85)/6$

Explanation:

$y = 3 m^{2} - 7 m - 3 = 0$ $y = 3m^2 - 7m - 3 = 0$
Use the improved quadratic formula (Socratic Search)
$D = d^{2} = b^{2} - 4 a c = 49 + 36 = 85$ $D = d^2 = b^2 - 4ac = 49 + 36 = 85$ --> $d = \pm \sqrt{85}$ $d = +- sqrt85$
There are 2 real roots:

$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{7}{6} \pm \frac{\sqrt{85}}{6} = \frac{7 + \sqrt{85}}{6}$ $x = -b/(2a) +- d/(2a) = 7/6 +- sqrt85/6 = (7 + sqrt85)/6$

NOTE
Using the improved quadratic formula is simpler and easier in computing the results.

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How do you solve $3 m^{2} - 7 m = 3$ $3m^2 - 7m = 3$ using the quadratic formula?

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How do you solve $3 m^{2} - 7 m = 3$ $3m^2 - 7m = 3$ using the quadratic formula?