Explicação passo-a-passo:

a) 4x² - 144x = 0

∆= b²- 4. a. c

∆ = (-144)² -4 . 4 . 0 = 20736 - 0 = 20736

x=

[tex] \frac{ - ( - 144) + - \sqrt{20736} }{2 \times 4} [/tex]

x' =

[tex] \frac{144 + 144}{8} = \frac{288}{8} = 36[/tex]

x'' =

[tex] \frac{144 - 144}{8} = \frac{0}{8} = 0[/tex]

b) x² - 2x = 0

∆= b²- 4. a. c

∆= (-2)²- 4. 1. 0

∆= 4

x =

[tex] \frac{ - ( - 2) + - \sqrt{4} }{2 \times 1} [/tex]

x' =

[tex] \frac{2 + 2}{2} = \frac{4}{2} = 2[/tex]

x'' =

[tex] \frac{2 - 2}{2} = \frac{0}{2} = 0[/tex]

c)

[tex] \frac{ {x}^{2} }{4} - \frac{3x}{2} = 0[/tex]

2x² - 3x = 0

∆= b²- 4. a. c

∆= (-3)²- 4. 2. 0

∆ = 9

x = -(-3) +- ✓9 /2 x 2

x' = 3+3 / 4 = 6/4 = 3/2

x'' = 3-3 /4 = 0

d) -x² + 25x = 0

∆= b²- 4. a. c

∆= 25²- 4. (-1). 0

∆= 625

x = -25 +- ✓625 / -2

x' = -25 + 25 / -2 = 0 / -2 = 0

x'' = -25 -25 / -2 = -50 / -2 = 25