Respuesta :

[tex]f(x)=5x^2-3\\\\\\ f(x+a)=5(x+a)^2-3=5(x^2+2ax+a^2)-3=\\\\=\boxed{5x^2+10ax+5a^2-3}[/tex]

On the other hand:

[tex]f(x+a)=5x^2+30x+42[/tex]

so:

[tex]10ax=30x\\\\10a=30\qquad|:10\\\\\boxed{a=3}[/tex]

Answer C.