Question

5x² - 11x = 12

Explanation:

Step1: Rearrange to standard quadratic form

$5x^2 - 11x - 12 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=5$, $b=-11$, $c=-12$.
$$x=\frac{-(-11)\pm\sqrt{(-11)^2-4(5)(-12)}}{2(5)}$$

Step3: Calculate discriminant

$\sqrt{121 + 240}=\sqrt{361}=19$

Step4: Solve for x values

$x=\frac{11+19}{10}=\frac{30}{10}=3$; $x=\frac{11-19}{10}=\frac{-8}{10}=-\frac{4}{5}$

Answer:

$x=3$ and $x=-\frac{4}{5}$