x, y - the numbers
The numbers add up to 7.
[tex]x+y=7 \\
y=7-x[/tex]
The numbers multiply to -30.
[tex]xy=-30 \\
\hbox{substitute 7-x for y:} \\
x(7-x)=-30 \\
7x-x^2=-30 \\
-x^2+7x+30=0 \\
-x^2-3x+10x+30=0 \\
-x(x+3)+10(x+3)=0 \\
(-x+10)(x+3)=0 \\
-x+10=0 \ \lor \ x+3=0 \\
x=10 \ \lor \ x=-3 \\ \\
y=7-x \\
y=7-10 \ \lor \ y=7-(-3) \\
y=-3 \ \lor \ y=10 \\ \\
(x,y)=(10,-3) \ or \ (-3,10)[/tex]
-3 and 10 add up to 7 and multiply to -30.
