Answer:
x = -
, x = 1
Explanation:
I assume you require the solution to the equation
2x² + x - 3 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 1
the factors are - 2 and + 3
use these factors to split the x- term
2x² - 2x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(2x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ( add 1 to each side )
x = 1
2x + 3 = 0 ( subtract 3 from each side )
2x = - 3 ( divide each side by 2 )
x = -

solutions are x = -
, x = 1