Question

formula sheet
solve the equation for x.
$5x^{2}-4x=6$
a. $x = \frac{-2 \pm \sqrt{26}}{5}$
b. $x = \frac{-2 \pm \sqrt{34}}{5}$
c. $x = \frac{2 \pm \sqrt{26}}{5}$
d. $x = \frac{2 \pm \sqrt{34}}{5}$

Explanation:

Step1: Rearrange to standard quadratic form

$5x^2 - 4x - 6 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=5$, $b=-4$, $c=-6$

Step3: Apply quadratic formula

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

Step4: Substitute coefficients

$x = \frac{-(-4) \pm \sqrt{(-4)^2-4(5)(-6)}}{2(5)}$

Step5: Simplify the expression

$x = \frac{4 \pm \sqrt{16+120}}{10} = \frac{4 \pm \sqrt{136}}{10} = \frac{4 \pm 2\sqrt{34}}{10} = \frac{2 \pm \sqrt{34}}{5}$

Answer:

D. $x = \frac{2 \pm \sqrt{34}}{5}$