we know that
using a graph tool
let's proceed to graph each case to determine the roots
case 1) \(2x^{2} - 16x + 12 = 0\)
the roots are
\(x1=0.8\ x2=7.2\) ------> is not the solution
see the attached figure N \(1\)
case 2) \(2x^{2} +8x -24 = 0\)
the roots are
\(x1=-6\ x2=2\)
see the attached figure N \(2\) --------> is the solution
case 3) \(3x^{2} - 4x - 12 = 0\)
the roots are
\(x1=-1.4\ x2=2.8\)------> is not the solution
see the attached figure N \(3\)
case 4) \(3x^{2} +12x +36 = 0\)
the graph does not have x-intercepts
see the attached figure N \(4\) ------> is not the solution
therefore
the answer is
the solution is
\(2x^{2} +8x -24 = 0\)
