а)

[tex]2 {x}^{2} + 3x - 2 = 0 \\ a = 2 \\ b = 3\\ c = - 2\\ D = {b}^{2} - 4ac = {3}^{2} - 4 \times 2 \times ( - 2) = 9 + 16 = 25 \\ x_{1} = \frac{ - 3 - 5}{2 \times 2} = - \frac{8}{4} = - 2\\ x_{2} = \frac{ - 3 + 5}{2 \times 2} = \frac{2}{4} = 0.5[/tex]

б)

[tex] {x}^{4} - 2 {x}^{2} - 24 = 0 \\ {x}^{2} = a, \: \: a \geqslant 0 \\ {a}^{2} - 2a - 24 = 0[/tex]

По теореме Виета:

[tex] {x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c [/tex]

[tex]a _{1}+ a_{2} =2 \\ a_{1}a _{2}= - 24\\ a _{1}=6 \\ a_{2} = - 4[/tex]

Второй корень не подходит

[tex] {x}^{2} = 6 \\ x_{1} = \sqrt{6} \\ x_{2} = - \sqrt{6} [/tex]