a)
3(x-\sqrt{3})^2-5(x-\sqrt{3})+2=0
3(x^2-2\sqrt3x+3)-5x+5\sqrt3+2=0
3x^2-6\sqrt3x+9-5x+5\sqrt3+2=0
3x^2-6\sqrt3x-5x+11+5\sqrt3=0
3x^2-(6\sqrt3+5)x+11+5\sqrt3=0
a=3 , b=-(6\sqrt3+5) , c=11+5\sqrt3
\Delta=b^2-4ac=[-(6\sqrt3+5)]^2-12(11+5\sqrt3)=
=36*3+60\sqrt3+25-132-60\sqrt3=1
\sqrt\Delta=1
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{6\sqrt3+5-1}{2*3}=\frac{6\sqrt3+4}{6}=\sqrt3+\frac{4}{6}=\sqrt3+\frac{2}{3}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{6\sqrt3+5+1}{6}=\frac{6\sqrt3+6}{6}=\sqrt3+1