Solve the equation $- 6 x^{2} - 24 = - 18 x$ $-6x^2-24=-18x$ ?

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Answer 1 · 2016-10-31T16:35:10

$x = \frac{3}{2} \pm \frac{\sqrt{7}}{2} i$ $x=3/2+-sqrt7/2i$

$- 6 x^{2} - 24 = - 18 x$ $-6x^2-24=-18x$

$\Leftrightarrow 6 x^{2} - 18 x + 24 = 0$ $hArr6x^2-18x+24=0$ and dividing by $6$ $6$ , we get

$x^{2} - 3 x + 4 = 0$ $x^2-3x+4=0$

$x^{3} - 2 \times \frac{3}{2} \times x + {(\frac{3}{2})}^{2} - {(\frac{3}{2})}^{2} + 4 = 0$ $x^3-2×3/2×x+(3/2)^2-(3/2)^2+4=0$

or ${(x - \frac{3}{2})}^{2} - \frac{9}{4} + 4 = 0$ $(x-3/2)^2-9/4+4=0$

or ${(x - \frac{3}{2})}^{2} - (- \frac{7}{4}) = 0$ $(x-3/2)^2-(-7/4)=0$

or ${(x - \frac{3}{2})}^{2} - {(\frac{\sqrt{7}}{2} i)}^{2} = 0$ $(x-3/2)^2-(sqrt7/2i)^2=0$

or $(x - \frac{3}{2} + \frac{\sqrt{7}}{2} i) (x - \frac{3}{2} - \frac{\sqrt{7}}{2} i) = 0$ $(x-3/2+sqrt7/2i)(x-3/2-sqrt7/2i)=0$

i.e. $x = \frac{3}{2} \pm \frac{\sqrt{7}}{2} i$ $x=3/2+-sqrt7/2i$

Solve the equation −6x2−24=−18x-6x^2-24=-18x?