4=7-2k+2/k-7

Solution for 4=7-2k+2/k-7 equation:

4=7-2k+2/k-7

We move all terms to the left:

4-(7-2k+2/k-7)=0


Domain of the equation: k-7)!=0

k∈R


We add all the numbers together, and all the variables

-(-2k+2/k)+4=0

We get rid of parentheses

2k-2/k+4=0

We multiply all the terms by the denominator


2k*k+4*k-2=0

We add all the numbers together, and all the variables

4k+2k*k-2=0

Wy multiply elements

2k^2+4k-2=0

a = 2; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·2·(-2)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*2}=\frac{-4-4\sqrt{2}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*2}=\frac{-4+4\sqrt{2}}{4}
$