How to solve x? 6^x + x^2 = 18

6^x + x^2 = 18 ; solve for x step by step.

6^x = 18 - x^2
6^x > 0 for any real x then 18-x^2 must be positive then x in ( - 3√2 , + 3√2)
Intersection between graph of y = 6^x and graph of 18-x^2 is a set of two point
{ Or study sign of first derivative of f(x) = 6^x + x^2 - 18 }
You may find a solution using a numeric method ( I used Newton)
x = 1.5348603058 . . .
Or
x = - 4.2425818073 . .

P.S.
Details for Newton's Method
iterative formula is x-f(x)/f'(x)
. . . . . . . . . . f(x) . . . . . . . . . . . . . . . . . . f ' (x) . . . . . . . . . . . . . . . . . . x
. . . . . . . . . -16.83333333333. . . . . . -1.70137342180. . . . . . -1.00000000000
x-f(x)/f'(x) 100.67852780125. . . . . . -21.78793498548. . . . . . -10.89396749573
x-f(x)/f'(x) 21.35216112040. . . . . . -12.54623454301. . . . . . -6.27312904232
x-f(x)/f'(x) 2.89661292979. . . . . . -9.14200522434. . . . . . -4.57125099698
x-f(x)/f'(x) 0.10044622830. . . . . . -8.50793245439. . . . . . -4.25440443447
x-f(x)/f'(x) 0.00013949623. . . . . . -8.48430134648. . . . . . -4.24259824902
x-f(x)/f'(x) 0.00000000027. . . . . . -8.48426843674. . . . . . -4.24258180734
x-f(x)/f'(x) 0.00000000000. . . . . . -8.48426843667. . . . . . -4.24258180731
First 7 iterations