k^2-8k-48(k-12)=(0)

Solution for k^2-8k-48(k-12)=(0) equation:

k^2-8k-48(k-12)=(0)

We move all terms to the left:

k^2-8k-48(k-12)-((0))=0

determiningTheFunctionDomain
k^2-8k-48(k-12)-0=0

We add all the numbers together, and all the variables

k^2-8k-48(k-12)=0

We multiply parentheses

k^2-8k-48k+576=0

We add all the numbers together, and all the variables

k^2-56k+576=0

a = 1; b = -56; c = +576;
Δ = b2-4ac
Δ = -562-4·1·576
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{13}}{2*1}=\frac{56-8\sqrt{13}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{13}}{2*1}=\frac{56+8\sqrt{13}}{2}
$