Resposta:

[tex] \red{x_{1} = 0 \: \: \: \: x_{2} = 2 } \\ [/tex]

Explicação passo-a-passo:

[tex] \blue{5x {}^{2} + 10x = 0} \\ 5x {}^{2} + 10x = 0 \\x {}^{2} + 2x = 0 \\x {}^{2} + 2 \times 1x + 1 {}^{2} - 1 {}^{2} = 0 \\(x + 1) {}^{2} - 1 {}^{2} = 0 \\x {}^{2} + 2x = 0 \\(x + 1) {}^{2} - 1 {}^{2} = 0 \\(x + 1) {}^{2} = 1 {}^{2} \\ (x + 1) {}^{2} = 1 \\ x + 1 = + \sqrt{1} \\ x + 1 = + 1 \\ x = + 1 - 1 \\ x + 1 = + \sqrt{1} \\ x = + 1 - 1 \\ x = - 1 + 1 \\ x = - 1 - 1 \\ x = 0 \\ x = - 1 - 1 \\ 1 - 1 \\ - (1 + 1) \\ - 2 \\ x = 0 \\ x = - 1 - 1 \\ x = 0 \\ x = 2 \\ \ \purple{resposta} \\ \red{x = 0 } \\ \red{x = - 2} [/tex]