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$1){x}^{2} - 26x + 133 = 0 \\ d = 676 - 532 = 144 = 12 \\ x1 = \frac{26 - 12}{2} = \frac{14}{2} = 7$

$x2 = \frac{26 + 12}{2} = \frac{38}{2} = 19$

$x1 + x2 = 7 + 19 = 26$

$x1 \times x2 = 7 \times 19 = 133$

$2) {x}^{2} - 7x - 30 = 0 \\ d = 49 + 120 = 169 = 13 \\ x1 = \frac{7 - 13}{2} = - \frac{6}{2} = - 3$

$x2 = \frac{7 + 13}{2} = \frac{20}{2} = 10$

$x1 + x2 = - 3 + 10 = 7 \\ x1 \times x2 = - 3 \times 10 = - 30$

$3) {x}^{2} - 18x + 45 = 0 \\ d = 324 - 180 = 144 = 12 \\ x1 = \frac{18 - 12}{2} = \frac{6}{2} = 3$

$x2 = \frac{18 + 12}{2} = \frac{30}{2} = 15$

$x1 + x2 = 3 + 15 = 18 \\ x1 \times x2 = 3 \times 15 = 45$

${x}^{2} - 12x - 28 = 0 \\ d = 144 + 112 = 256 = 16 \\ x1 = \frac{12 - 16}{2} = - \frac{4}{2} = - 2$

$x2 = \frac{12 + 16}{2} = \frac{28}{2} = 14$

$x1 + x2 = - 2 + 14 = 12 \\ x1 \times x2 = - 2 \times 14 = - 28$