Question

need help.    solve for y.  try factoring first if not possible or difficult use quadratic formula.               y²-6y+6=0

Answer 1

$y^2-6y+6=0\\ y^2-6y+9-3=0\\ (y-3)^2=3\\ |y-3|=\sqrt3\\ y-3=\sqrt3 \vee y-3=-\sqrt3\\ y=3+\sqrt3 \vee y=3-\sqrt3$

Answer 2

$y^2-6y+6=0\\ \\a=1 , \ b=-6, \ c=6 \\ \\\Delta =b^2-4ac = (-6)^2 -4\cdot1\cdot6 = 36-24=12\\ \\\sqrt{\Delta }= \sqrt{12}=\sqrt{4\cdot 3}=2\sqrt{3} \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{6-2\sqrt{3}}{2 }=\frac{2( 3- \sqrt{3})}{2}= 3- \sqrt{3}$

$x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{6+2\sqrt{3}}{2 }=\frac{2( 3+ \sqrt{3})}{2}= 3+ \sqrt{3}$