Solutions to the quadratic equation x squared-5x-24=0

X^2-5x-24=0  

A quadratic of the form ax^2+bx+c can be factored by finding values j and k which satisfy two conditions, jk=ac and j+k=b, in this case:

ac=jk=-24 and b=j+k=-5, so j and k must be 3 and -8

Now replace bx with jx and kx in the original equation:

x^2+3x-8x-24=0  and factor 1st and 2nd pair of terms...

x(x+3)-8(x+3)=0  which is equal to:

(x+3)(x-8)=0  so

x=-3 and 8