Question

1. $4x^{2}-x=5$

Explanation:

Step1: Rearrange to standard quadratic form

$4x^2 - x - 5 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=4$, $b=-1$, $c=-5$

Step3: Apply quadratic formula

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

Step4: Substitute values into formula

$$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(4)(-5)}}{2(4)}$$

Step5: Simplify discriminant

$\sqrt{1 + 80} = \sqrt{81} = 9$

Step6: Calculate two solutions

$x_1 = \frac{1 + 9}{8} = \frac{10}{8} = \frac{5}{4}$
$x_2 = \frac{1 - 9}{8} = \frac{-8}{8} = -1$

Answer:

$x = \frac{5}{4}$ or $x = -1$