Solve 3 x^2 - 4x + 20 3 = 0 - Vidyadip

Question

Solve $3{x^2} - 4x + \frac{{20}}{3} = 0$

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Answer

Here $3{x^2} - 4x + \frac{{20}}{3} = 0$
Comparing the given quadratic equation with $ax^2 + bx + c = 0$, we have
a = 3, b = -4 and $c = \frac{{20}}{3}$
$\therefore x = \frac{{ - ( - 4) \pm \sqrt {{{( - 4)}^2} - 4 \times 3 \times \frac{{20}}{3}} }}{{2 \times 3}}$$ = \frac{{4 \pm \sqrt {16 - 80} }}{6}$
$ = \frac{{4 \pm \sqrt { - 64} }}{6} = \frac{{4 \pm 8\sqrt { - 1} }}{6} = \frac{{4 \pm 8i}}{6}$$ = \frac{{2 \pm 4i}}{3}$
Thus $x = \frac{{2 + 4i}}{3}$ and $x = \frac{{2 - 4i}}{3}$

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