Solve for x: (3x+7)(x-1)=24.

To solve for x:
(3x+7)(x-1)=24.

We expand left  and rewrite the
equation:

3x(x-1)+7(x-1) =
24.

3x^2-3x+7x-7 =
24.

=> 3x^2 +4x-7-24 =
0.

=> 3x^2 +4x-31 =
0....(1).

This is in the form of ax^2+bx+c = 0 whose
solution is given by:

x1 = (-b+sqrt(b^2-4ac)}/2a
and

x2 =
(-b-sqrt(b^2-4ac)}/2a.

Here in equation at (1): a = 3, b= 4
and c = -31.

Therefore x1 = (-4+sqrt(4^2-4*3*-31)}/2*3 =
(-4+sqrt388)/6

=> x1 =
(-2+sqrt97)/3

x2 =
(-2-sqrt97)/3.

Therefore  (-2+sqrt97)/3 and (-2-sqrt97)/3
are the solutions.