Question

Find all possible solutions. give your answers in increasing order. give your answers to the nearest thousandth. \sqrt{-5 x + 6} + 3 = 4 x

Answer 1

Hello,


`√(6-5x) +3=4x\\\\ √(6-5x) =4x-3 \\\\ 6-5x=(4x-3)^2\\\\ 6-5x=16x^2-24x+9\\\\ 16x^2-19x+3=0\\\\ \Delta=19^2-4*3*19=169=13^2\\\\ x= (19+13)/(32) =1\ or\ x=(19-13)/(32) = (3)/(16) \\\\ If\ x=1\ then\ √(6-5) +3=4*1\ ==\ \textgreater \ 1+3=4 \\\\ If\ x=(3)/(16)\ then\ \sqrt{6-5*(3)/(16)} +3=4*(3)/(16)\ ==\ \textgreater \ (21)/(4) \\eq (3)/(4) \\ Solution=\{1\}`