Let us consider an example to understand it better. Suppose we have two functions given as: F (x) = 3x - 7 and G (x) = x2 + 4x – 27. First step is to equate both functions to get the equation: 3x - 7 = x2 + 4x - 27.
As we can see that LHS is in simplified form, no more calculations are required here. Let us combine LHS with RHS to get a resultant Quadratic Equation: x2 + x - 20 = 0. This is in standard form of a quadratic equation.
We can now factor this equation as: x2 + x - 20 = (x - 4) (x + 5), and then equating factors to zero we get: x = 4 and x = -5.
Substitute values of ”x” in original function equations of F (x) and G (x) to verify that they have same corresponding 'y; values. In this example, at x = 4 and x = -5 we get y = -5 and y = 22 from both the equations. Thus their point of intersection is: (-5, -22).