1. The solution of the quadratic inequalities are the ranges of values which satisfied the inequalities itself.
2. There are 2 methods to solve the inequalities.
1. Graph method
2. Number line method

Step to solve a Quadratic Inequalities
Step 1 : Rewrite the inequality with zero on one side and make sure a > 0
Step 2 : Find where it crosses the x-axis  (Put y = 0)
Step 3 : Sketch the graph and shade the region to find the range of values of  x

Example
Find the range of values of x for each of the following :
(a) ${x}^{2}-4x+3<0$
(b) $12+10x-2{x}^{2}<0$

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Solving Quadratic Inequalities – The Basics