Question

What are the roots of the equation?
2x^2+x=6

Answer 1

x = - 2, x =
`(3)/(2)`

Explanation:

Given

2x² + x = 6 ( subtract 6 from both sides )

2x² + x - 6 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = + 1

The factors are + 4 and - 3

Use these factors to split the x- term

2x² + 4x - 3x - 6 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) - 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`

Answer 2

They would be 3/2 & -2.