Question 176691
The area of a triangle is given by {{{A=(bh)/2}}}.  Let the measure of the base be {{{x}}}, then we are given that the altitude is {{{2x - 3}}}, so {{{A(x) = (x (2x - 3))/2}}} and we are given that the area of this particular triangle is 126 square centimeters.  Therefore:


{{{(x (2x - 3))/2 = 126}}}


{{{(2x^2 - 3x)/2 = 126}}}


{{{2x^2 - 3x = 252}}}


{{{2x^2 - 3x - 252 = 0}}}


Solve the quadratic by ordinary means.  You can factor, complete the square, or use the quadratic formula -- all three methods work.  You will get two roots as you should expect, except that one of them will be < 0.  This absurd result for the measure of a side of a triangle is an extraneous root caused by squaring the variable in the process of solving the problem.  Exclude the negative root.  The positive root is your answer.