# How do you solve #7+13x - 2x^2>0#?

##### 1 Answer

D = d^2 = 169 + 56 = 225 -> d = +- 15.

x = -13/-4 +- 15/-4

x = 13/4 +- 15/4

x1 = 28/4 = 7

x2 = -2/4 = -1/2

---------------|-1/2==|0==========|7-------------------

**Test point method** . Plot

**Algebraic method** . Between the 2 real roots

NOTE. When a is negative (< 0), the parabola opens downward. Between the 2 real roots, a part of the parabola is above the x-axis, meaning, f(x) is positive (> 0) in this segment, as opposite in sign to a(< 0).

The algebraic method is very fast, because you don't have to draw the number line each time. Just look at the side of a, you would easily know where is the solution set.