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

Oct 31, 2016

$x = \frac{3}{2} \pm \frac{\sqrt{7}}{2} i$

#### Explanation:

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

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

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

x^3-2×3/2×x+(3/2)^2-(3/2)^2+4=0

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

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

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

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

i.e. $x = \frac{3}{2} \pm \frac{\sqrt{7}}{2} i$