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,

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