What are the solutions of the given equation 2x^2+9x+10=0

Answer:see explanationStep-by-step explanation:Given2x² + 9x + 10 = 0To factor the quadraticConsider 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 × 10 = 20 and sum = + 9The factors are + 4 and + 5Use these factors to split the x- term2x² + 4x + 5x + 10 = 0 ( factor the first/second and third/fourth terms )2x(x + 2) + 5(x + 2) = 0 ← factor out (x + 2) from each term(x + 2)(2x + 5) = 0Equate each factor to zero and solve for xx + 2 = 0 ⇒ x = - 22x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]