SOLUTION: SOlve this linear equation: {{{3*x^2 - 6x - 5 > 0}}}

Algebra ->  Graphs -> SOLUTION: SOlve this linear equation: {{{3*x^2 - 6x - 5 > 0}}}      Log On


   

Question 702644: SOlve this linear equation:
3%2Ax%5E2+-+6x+-+5+%3E+0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What are the zeros of the quadratic expression? Those are critical points for the inequality. They help you find your solution intervals.
Being brief, x+=+%286+%2B-+sqrt%28+36-4%2A3%2A%28-5%29+%29%29%2F%286%29+
x=1%2B-+%282%2F3%29%2Asqrt%286%29

The x^2 term shows that parabola opens upward and therefore has a minimum. The minimum will be between the interval x=1-(2/3)(6)^(1/2) and x=1+(2/3)(6)^(1/2). This minimum being below the horizontal axis, is negative so this interval does NOT satisfy the inequality.

The solution is therefore, x%3C1-%282%2F3%29%2Asqrt%286%29 or x%3E1%2B%282%2F3%29%2Asqrt%286%29