1/2k+2=5+5-6k

Solution for 1/2k+2=5+5-6k equation:

1/2k+2=5+5-6k

We move all terms to the left:

1/2k+2-(5+5-6k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We add all the numbers together, and all the variables

1/2k-(-6k+10)+2=0

We get rid of parentheses

1/2k+6k-10+2=0

We multiply all the terms by the denominator


6k*2k-10*2k+2*2k+1=0

Wy multiply elements

12k^2-20k+4k+1=0

We add all the numbers together, and all the variables

12k^2-16k+1=0

a = 12; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·12·1
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{13}}{2*12}=\frac{16-4\sqrt{13}}{24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{13}}{2*12}=\frac{16+4\sqrt{13}}{24}
$