Solve for x:2^x=x^2

2^x = 2x

no simple formula method to do this type of equation.
If you know Calculus , you could use Newton's method.

A good way to start is to graph
y = 2^x and y = x^2 to see that there are two intersection points.

However, they made it easy for you and picked a system with nice numbers.
A bit of inspection would show that if x = 2
LS = 2^2 = 4
RS = 2^2 = 4 , so x = 2 is a solution

also for x = 4
LS = 2^4 = 16
RS = 4^2 = 16 , so x = 4 is the other solution

has your equation been : 3^x = x^2 , it would be a totally different story, and very messy