Question

$2x^2 + x - 6 = 0$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=2$, $b=1$, $c=-6$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:

$$ x=\frac{-1\pm\sqrt{1^2-4\times2\times(-6)}}{2\times2} $$

Step3: Calculate discriminant

Compute $b^2-4ac$:

$$ 1 - (-48) = 49 $$

Step4: Solve for x values

Substitute discriminant result:

$$ x=\frac{-1\pm7}{4} $$

Split into two solutions:
$x_1=\frac{-1+7}{4}=\frac{6}{4}=\frac{3}{2}$
$x_2=\frac{-1-7}{4}=\frac{-8}{4}=-2$

Answer:

$x=\frac{3}{2}$ or $x=-2$