Question

$2x^2 - 3x - 5 = 0$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=2$, $b=-3$, $c=-5$

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

$b^2-4ac=(-3)^2-4\times2\times(-5)=9+40=49$

Step4: Substitute and solve for x

$x=\frac{3\pm\sqrt{49}}{2\times2}=\frac{3\pm7}{4}$

Answer:

$x=\frac{5}{2}$ or $x=-1$