Question

solve the equation:
$2 x {}^{2} + x - 6 = 0$
​

Answer 1

Solve by factoring

$\sf\implies 2x^2 + x - 6 = 0$

$\sf \implies 2x^2 + 4x - 3x - 6$

$\sf \implies 2x(x+2) -3(x+2)$

$\sf \implies (2x-3)(x+2)$

First solution

→ 2x - 3 = 0

→ 2x = 3

$\bigstar\boxed{\sf x = \dfrac{3}{2}}\bigstar$

Second solution

x + 2 = 0

$\bigstar\boxed{\sf x = -2}\bigstar$

_________________________

Solve by using quadratic formula

2x² + x - 6 = 0

a = 2 , b = 1 , c = -6

Quadratic Formula:-

$\qquad \qquad \qquad \bigstar\boxed{\sf x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\bigstar$

$\sf\implies x = \dfrac{-1 \pm \sqrt{(1)^2 - 4(2)(-6)}}{2(2)}$

$\sf\implies x = \dfrac{-1 \pm \sqrt{1+48}}{4}$

$\sf\implies x = \dfrac{-1 \pm \sqrt{49}}{4}$

$\sf\implies x = \dfrac{-1 \pm 7}{4}$

$\sf\implies x = \dfrac{3}{2} \qquad \qquad Or \; \; x = -2$

Hope it helps

Answer 2

2x^2 + x - 6 = 0
2x^2 + 4x - 3x - 6 =0
2x ( x + 2 ) - 3 ( x + 2 ) = 0
( 2x - 3 ) =0. ( x + 2 ) = 0
X = 3/2. X = -2

Negative value never exists so the value of x =3/2



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