2x² + 5x - 3 = 0
Multiply the coeeficient of x² and the constant (-3)
That is 2 ( - 3) = -6
Find the numbers whose sum is 5 and whose product is -6
The number is 6 and -1
Replace 5x by the numbers
2x² + 6x - x - 3 = 0
2x( x + 3) - 1 ( x + 3) = 0
(2x - 1 ) ( x + 3) = 0
Either 2x -1 = 0 or x + 3 = 0
2x = 1
x = 1/2 or x = -3