1/2k+6=4k-8

Solution for 1/2k+6=4k-8 equation:

1/2k+6=4k-8

We move all terms to the left:

1/2k+6-(4k-8)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

1/2k-4k+8+6=0

We multiply all the terms by the denominator


-4k*2k+8*2k+6*2k+1=0

Wy multiply elements

-8k^2+16k+12k+1=0

We add all the numbers together, and all the variables

-8k^2+28k+1=0

a = -8; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-8)·1
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{51}}{2*-8}=\frac{-28-4\sqrt{51}}{-16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{51}}{2*-8}=\frac{-28+4\sqrt{51}}{-16}
$