Find length (requires quadratic equation)

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There is an equation $l = 4\sqrt{(\frac{w^2+d^2}{4})+(h-k)^2}$

Following values are given

$l = 50$

$w = 12$

$d = 10$

$k = 3$

What is $h$?

Following choices are

$14$

$10$

$11$

$12$

$13$

My answers come nothing near these!

Here is what I am doing, please assist

TL;DR: $b = 27.75, b=8.245$


$50 = 4\sqrt{(\frac{w^2+d^2}{4})+(h-k)^2}$

$50 = 4\sqrt{(\frac{12^2+10^2}{4})+(h-3)^2}$

$50 = 4\sqrt{(\frac{244}{4})+h^2-6h+9^2}$

$50 = 4\sqrt{61+h^2-6h+9}$

$50 = 4\sqrt{70+h^2-6h}$

Divide both sides by $4$

$12.5 = \sqrt{70+h^2-6h}$

Raise both sides by power of $2$

$156.25 = 70+h^2-6h$

$0 = 70+h^2-6h - 156.25$

$0 = h^2 - 6h - 86.25$

Now, solve for $h$ with quadratic equation

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

$\frac{-(-6)\pm\sqrt{(-6)^2-4(-86.25)}}{2}$

$\frac{36\pm\sqrt{36+345}}{2}$

$\frac{36\pm\sqrt{381}}{2}$

$\frac{36 \pm 19.51}{2}$

$b = 27.75, b=8.245$

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From $$\frac{-(-6)\pm\sqrt{(-6)^2-4(-86.25)}}{2}$$

to $$\frac{36\pm\sqrt{36+345}}{2}$$

You have written $36$ for $-(-6)$. If you fix that, what you will find is $h_1 = -6.7596$ and $h_2 = 12.76$. I don't know if question wants you to round it up but with given values, these are the values that $h$ can take.