Question

find the real solution of the equation by graphing
6x^3-2x=-9x^2

i got 0.2,-1.7 is this correct

Answer 1

6 x ^ 3 - 2 x = - 9 x ^ 2 Add 9 x ^ 2 to both sides

6 x ^ 3 - 2 x + 9 x ^ 2 = - 9 x ^ 2 + 9 x ^ 2

6 x ^ 3 + 9 x ^ 2 - 2 x = 0

x * ( 6 x ^ 2 + 9 x - 2 )= 0

You equation have 3 solutions:

Obviously solution x = 0

Equation :

6 x ^ 2 + 9 x - 2 = 0

have two solutions :

x1/2= [ - 9 + OR - sqrt ( 129 ) ] / 12


3 solutions are :

x1 = 0

x2 = [ - 9 + sqrt ( 129 ) ] / 12

x3 = [ - 9 - sqrt ( 129 ) ] / 12


Your two soutions are correct but polinomial equation of degre 3 have 3 solutions.

Oneof solutions are x = 0

Answer 2

thank you for checking and helping