The solution is as beautiful as the problem.

[@ugomikechinonso]

Good work

[@justmathsbymike]

Thanks

[@patk5724]

I was kinda wondering if you could conclude that
-2x^2 = -2, would it actually comply with the law of property[ a^a = b^b, complies that a = b
-2x^2 = -2
x^2 = 1
x = 1 or -1
This is just to prevent you from further using the lambert W function to solve equation.

[@justmathsbymike]

I see what you mean. Actually, I didn't notice that after multiplying both sides by -2, I could apply that a^a =b^b property.
But the Lambert W function helps with a wider range of equations than what we're solving here.
Nevertheless, I am grateful for showing me that simple approach.