Question 95037
2x^2+5x-3=0

First you must factor 2x^2+5x-3:
1.  Multiply the first and last coefficients:  2 x -3 = -6
2.  Find two multiples of -6 that can be added to get 5.
3.  The two multiples are 6 and -1  {6x-1=-6 and 6+(-1)=5}
4.  Use the two multiples to help you write two binomials:  (x+6)(x+-1)
5.  Since there is a 2 in front of the x^2 term, divide the 6 and -1 by the 2.  
6.  You will have . . . (x + 3)(x + -1/2)
7.  Since you should have all whole numbers and not fractions, take the 2 from the denominator and put it in front of the 2, and thus you will have the factored from of 2x^2+5x-3:
   (x + 3)(2x + -1)

Now to solve:
1.  Set each of the binomials to equal zero, and solve for x.
x+3 = 0   x = -3

2x + -1 = 0  
2x = 1
x = 1/2