$a\text{)}3x^2-5x+2=0$  

$\Delta ={\left(-5\right)}^2-4\cdot 3\cdot 2=25-24=1$  

$\sqrt{\Delta }=1$  

$x_1=\frac{5-1}{2\cdot 3}=\frac{4}{6}=\frac{2}{3}$  

$x_2=\frac{5+1}{2\cdot 3}=\frac{6}{6}=1$  

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$b\text{)}-2x^2-4x+3=0$  

$\Delta ={\left(-4\right)}^2-4\cdot \left(-2\right)\cdot 3=16+24=40$  

$\sqrt{\Delta }=2\sqrt{10}$  

$x_1=\frac{4-2\sqrt{10}}{2\cdot \left(-2\right)}=\frac{4-2\sqrt{10}}{-4}=\frac{\sqrt{10}-2}{2}$  

$x_2=\frac{4+2\sqrt{10}}{2\cdot \left(-2\right)}=\frac{4+2\sqrt{10}}{-4}=\frac{-2-\sqrt{10}}{2}$  

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$c\text{)}9x^2-12\sqrt{5}x+20=0$  

$\Delta ={\left(-12\sqrt{5}\right)}^2-4\cdot 9\cdot 20=720-720=0$  

$\sqrt{\Delta }=0$  

$x=\frac{12\sqrt{5}}{2\cdot 9}=\frac{12\sqrt{5}}{18}=\frac{2\sqrt{5}}{3}$  

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$d\text{)}{x}^2-3\cdot 2^{16}x+2^{33}$  

$\Delta ={\left(-3\cdot 2^{16}\right)}^2-4\cdot 1\cdot 2^{33}=9\cdot 2^{32}-2^{35}=2^{32}\left(9-2^3\right)=2^{32}\cdot \left(9-8\right)=2^{32}$  

$\sqrt{\Delta }=2^{16}$  

$x_1=\frac{3\cdot 2^{16}-2^{16}}{2}=\frac{2^{16}\cdot \left(3-1\right)}{2}=\frac{2^{16}\cdot 2}{2}=2^{16}$  

$x_2=\frac{3\cdot 2^{16}+2^{16}}{2}=\frac{2^{16}\cdot \left(3+1\right)}{2}=\frac{2^{16}\cdot 4}{2}=2^{17}$  

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$e\text{)}{2}^{11}{x}^2-3^{5}x+2^{17}=0$  

$\Delta ={\left(-3^5\right)}^2-4\cdot 2^{11}\cdot 2^{17}=3^{10}-2^{30}<0$  

To równanie nie ma rozwiązań.

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$f\text{)}{x}^2-\left(3^{20}+1\right)x+3^{20}=0$  

$\Delta ={\left(-\left(3^{20}+1\right)\right)}^2-4\cdot 1\cdot 3^{20}={\left(3^{20}+1\right)}^2-4\cdot 3^{20}=$  

$=3^{40}+2\cdot {30}^{20}+1-4\cdot 3^{20}=3^{40}-2\cdot 3^{20}+1={\left(3^{20}-1\right)}^2$  

$\sqrt{\Delta }=3^{20}-1$  

$x_1=\frac{3^{20}+1-3^{20}+1}{2}=\frac{2}{2}=1$  

$x_2=\frac{3^{20}+1+3^{20}-1}{2}=\frac{2\cdot 3^{20}}{2}=3^{20}$