How do I find the solutions to an equation?

Question

Find the solutions to the equation -1/2x² = -6x + 20

Answer 1

Multiplies both sides by -2:

x^2 = 12x - 40

x^2 - 12x + 40 = 0

x = [12 +or- sqrt( 144 - 160)] / 2

= [ 12 +or- sqrt( -16)]/2

= [ 12 +or- 4i]/2

= 6 +or- 2i

check:

x^2 = (6+2i)(6+2i) = 36 + 24i - 4 = 32 + 24i

-1/2 x^2 = -16 - 12i <--- this is the left side

-6x = -36 - 12i

-6x + 20 = -16 - 12i <--- this is the right side

x=6 +or- 2i