How do you solve 2/3x^2+30=0?

Dec 28, 2016

$x = \pm 3 \sqrt{5} \textcolor{w h i t e}{.} i$

Explanation:

Subtract 30 from both sides

$\frac{2}{3} {x}^{2} = - 30$

Multiply both sides by $\frac{3}{2}$

${x}^{2} = - 45$

square root both sides

$x = \pm \sqrt{- 45}$

But $45 = 5 \times 9 = 5 \times {3}^{2}$ giving

$x = \pm 3 \sqrt{- 5}$

$x = \pm 3 \sqrt{5 \times - 1}$

But $\sqrt{- 1} = i$

$x = \pm 3 \sqrt{5} \textcolor{w h i t e}{.} i$