How can I solve this equation 5x^2-2x-6=-2x^2+9x

Add 2x^2 to both sides

7x^2-2x-6=9x

Subtract 9x from both sides

7x^2-11x-6=0

Factor by using slip and slide

x^2-11x-42

(x-14) (x+3)

(x-14/7) (x+3/7)

(x-2) (7x+3)

Then use the Zero Product Property to find roots

x-2=0

x=2

7x+3=0

7x=-3

x=-3/7

Final answer: x=-3/7, x=2