6m² – 4m = 3

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Solution

Given: 6m² – 4m = 3
On rewriting this equation in standard form of the quadratic equation, we get:
=>6m² – 4m – 3 = 0
On comparing this equation with am² + bm + c = 0, we get:
a = 6, b = –4, c = –3
For the quadratic equation am² + bm + c = 0 in variable m, the quadratic formula is
$m = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
On substituting a = 6, b = –4, c = –3, we get:

$m = \frac{- (- 4) \pm \sqrt{(- 4)^{2} - 4 (6) (- 3)}}{2 (6)} = \frac{4 \pm \sqrt{16 + 72}}{12} = \frac{4 \pm \sqrt{88}}{12} = \frac{4 \pm 2 \sqrt{22}}{12} = \frac{2 \pm \sqrt{22}}{6} Thus, the solution of the given quadratic equation is m = \frac{2 + \sqrt{22}}{6}, \frac{2 - \sqrt{22}}{6} .$

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