k=48/k-16

Solution for k=48/k-16 equation:

k=48/k-16

We move all terms to the left:

k-(48/k-16)=0


Domain of the equation: k-16)!=0

k∈R


We get rid of parentheses

k-48/k+16=0

We multiply all the terms by the denominator


k*k+16*k-48=0

We add all the numbers together, and all the variables

16k+k*k-48=0

Wy multiply elements

k^2+16k-48=0

a = 1; b = 16; c = -48;
Δ = b2-4ac
Δ = 162-4·1·(-48)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{7}}{2*1}=\frac{-16-8\sqrt{7}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{7}}{2*1}=\frac{-16+8\sqrt{7}}{2}
$