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[tex] \frac{ {x}^{2} }{2} - \frac{5x}{2} = - 3 \\ \\ {x}^{2} - 5x = - 3 \times 2 \\ {x}^{2} - 5x = - 6 \\ {x}^{2} - 5x + 6 = 0 \\ x = \frac{ - ( - 5) + - \sqrt{ {( - 5)}^{2} - 4 \times 1 \times 6} }{2 \times 1} \\ \\ x = \frac{5 + - \sqrt{25 - 24} }{2} \\ \\ x = \frac{5 + - \sqrt{1} }{2} \\ \\ x1 = \frac{5 + 1}{2} = \frac{6}{2} = 3 \\ \\ x2 = \frac{5 - 1}{2} = \frac{4}{2} = 2[/tex]

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[tex] \frac{ {x}^{2} }{4} - \frac{x}{3} = - \frac{1}{9} \\ \\ \frac{9 {x}^{2} - 12x = - 4}{36} \\ \\ 9 {x}^{2} - 12x + 4 = 0 \\ x = \frac{ - ( - 12) + - \sqrt{ {( - 12)}^{2} - 4 \times 9 \times 4} }{2 \times 9} \\ \\ x = \frac{12 + - \sqrt{144 - 144} }{18} \\ \\ x = \frac{12 + - \sqrt{0} }{18} \\ \\ x1 = x2 = \frac{12}{18} = \frac{2}{3} [/tex]

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[tex] \frac{ {x}^{2} }{2} - \frac{1}{5} = \frac{3x - 1}{5} \\ \\ \frac{5 {x}^{2} - 2 = 2(3x - 1) }{10} \\ \\ 5 {x}^{2} - 2 = 6x - 2 \\ 5 {x}^{2} - 6x - 2 + 2 = 0 \\ 5 {x}^{2} - 6x = 0 \\ x(5x - 6) = 0 \\ x1 = \frac{6}{5} \\ \\ x2 = 0[/tex]