$$\left(2\times 5^{\frac{1}{2}}-3\right)\left(3-\sqrt{5}\right)=11a\sqrt{5}-b$$

$$6\times 5^{\frac{1}{2}}-2\times 5^{\frac{1}{2}}\sqrt{5}-9+3\sqrt{5}=11a\sqrt{5}-b$$

$$11a\sqrt{5}-b=6\times 5^{\frac{1}{2}}-2\times 5^{\frac{1}{2}}\sqrt{5}-9+3\sqrt{5}$$

$$11a\sqrt{5}=6\times 5^{\frac{1}{2}}-2\times 5^{\frac{1}{2}}\sqrt{5}-9+3\sqrt{5}+b$$

$$11\sqrt{5}a=b-2\sqrt{5}\sqrt{5}+3\sqrt{5}+6\sqrt{5}-9$$

$$11\sqrt{5}a=b-2\times 5+3\sqrt{5}+6\sqrt{5}-9$$

$$11\sqrt{5}a=b-10+3\sqrt{5}+6\sqrt{5}-9$$

$$11\sqrt{5}a=b-10+9\sqrt{5}-9$$

$$11\sqrt{5}a=b-19+9\sqrt{5}$$

$$11\sqrt{5}a=b+9\sqrt{5}-19$$

$$\frac{11\sqrt{5}a}{11\sqrt{5}}=\frac{b+9\sqrt{5}-19}{11\sqrt{5}}$$

$$a=\frac{b+9\sqrt{5}-19}{11\sqrt{5}}$$

$$a=\frac{\sqrt{5}\left(b+9\sqrt{5}-19\right)}{55}$$

$$\left(2\times 5^{\frac{1}{2}}-3\right)\left(3-\sqrt{5}\right)=11a\sqrt{5}-b$$

$$6\times 5^{\frac{1}{2}}-2\times 5^{\frac{1}{2}}\sqrt{5}-9+3\sqrt{5}=11a\sqrt{5}-b$$

$$11a\sqrt{5}-b=6\times 5^{\frac{1}{2}}-2\times 5^{\frac{1}{2}}\sqrt{5}-9+3\sqrt{5}$$

$$-b=6\times 5^{\frac{1}{2}}-2\times 5^{\frac{1}{2}}\sqrt{5}-9+3\sqrt{5}-11a\sqrt{5}$$

$$-b=-2\sqrt{5}\sqrt{5}+3\sqrt{5}+6\sqrt{5}-9-11\sqrt{5}a$$

$$-b=-2\times 5+3\sqrt{5}+6\sqrt{5}-9-11\sqrt{5}a$$

$$-b=-10+3\sqrt{5}+6\sqrt{5}-9-11\sqrt{5}a$$

$$-b=-10+9\sqrt{5}-9-11\sqrt{5}a$$

$$-b=-19+9\sqrt{5}-11\sqrt{5}a$$

$$-b=-11\sqrt{5}a+9\sqrt{5}-19$$

$$\frac{-b}{-1}=\frac{-11\sqrt{5}a+9\sqrt{5}-19}{-1}$$

$$b=\frac{-11\sqrt{5}a+9\sqrt{5}-19}{-1}$$

$$b=11\sqrt{5}a+19-9\sqrt{5}$$