the dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other. The area of the resulting recatangle is 126 in2. What was the original side length of the square

Let
x--------> original length side of a square

we know that
area rectangle=length*width
area=126 in²
length=(x+8)
width=(x-3)
so
126=(x+8)*(x-3)------> x²-3x+8x-24=126----> x²+5x-150=0

using  a graph tool------> to resolve the second order equation
see the attached figure
the solution is
x=10 in

the answer is
the original length side of a square is 10 in