Since this is a quadratic equation, one way to solve it is by factoring. That does not always work, but this time it does work pretty easily.

This equation can factor down like this:

(2x-1)(x+5) = 0

You can see this is a correct factoring because you could multiply it out and get

2x^2+10x-x-5 = 0

And that simplifies to

2x^2+9x-5 = 0

So now you have to find the possible values of x.

If (2x-1)(x+5) = 0 the solutions are

x = -5

or

2x = 1 which means x = .5

So the solutions are x=-5 or x=.5

2x^2 + 9x - 5 = 0

The above is a quadratic equation i.e ax^2+bx+c=0, therefore we can apply the quadratic formula to it:

Where a = 2

b = 9

c = -5

Input the values in the above given formula

x=[-9+sqrt{(9)^2-4(2)(-5)}]/2(2) x=[-9-sqrt{(9)^2-4(2)(-5)}]/2(2)

=[-9+sqrt(81+40)]/4 =[-9-sqrt(81+40)]/4

=[-9+sqrt(121)]/4 =[-9-sqrt(121)]/4

=[-9+11]/4 =[-9-11]/4

= 2/4 =-20/4

= 0.5 = -5

**Solution set= (0.5,-5)**