$\frac{a}{b}=\frac{2}{5}\Rightarrow \frac{a}{2}=\frac{b}{5}\Rightarrow \frac{a}{2.4}=\frac{b}{5.4}$

$\frac{b}{c}=\frac{4}{3}\Rightarrow \frac{b}{4}=\frac{c}{3}\Rightarrow \frac{b}{4.5}=\frac{c}{5.3}$

$\Rightarrow \frac{a}{8}=\frac{b}{20}=\frac{c}{15}=k=\frac{a+b+c}{8+20+15}$ . Suy ra:

 a = 8k ; b = 20k ; c = 15k thay vào a.b - c$^{2}=-10,4.$ Ta có:

8k. 20k – (15k)$^{2}$ = -10,4 $\Rightarrow -65{{k}^{2}}=-10,4\Rightarrow k=\pm 0,4$

Vậy :

$\frac{a+b+c}{43}=\pm 0,4$

$\Rightarrow |a+b+c|=17,2$