If a quadratic equation has solutions
[tex]x=a,x=b[/tex]
Then
[tex]x-a=0\text{ and x-b=0}[/tex]
Furthermore, the quadratic can be written as
[tex]\begin{gathered} y=(x-a)(x-b) \\ where,y=0 \end{gathered}[/tex]
Therefore,
[tex](x-a)(x-b)=0[/tex]
Given:
[tex]a=-3,b=6[/tex]
Hence,
[tex]\begin{gathered} (x--3)(x-6)=0 \\ (x+3)(x-6)=0 \end{gathered}[/tex]
Simplify
[tex]\begin{gathered} x(x-6)+3(x-6)=0 \\ x^2-6x+3x-18=0 \\ x^2-3x-18=0 \end{gathered}[/tex]
Hence, the quadratic equation is
[tex]x^{2}-3x-18=0[/tex]
