What is/are the solution(s) to: sqrt(-9x+8)-9=8x

Question

Finding the value of X. Can be more than one answer.

Answer 1

sqrt(-9x+8)=8x+9; -9x+8=64x^2+144x+81; 64x^2+153x+73=0; x=(-153+sqrt(153^2-4*64*73))/128=-0.6585 or -1.7321. Of these solutions, only x=-0.6585 satisfies the original equation, because the other solution gives the negative square root when the positive root is implied (i.e., +sqrt(-9x+8)>0 but 8x+9<0, because 8x+9=-sqrt(-9x+8)).