1/2k+7=3k+6

Solution for 1/2k+7=3k+6 equation:

1/2k+7=3k+6

We move all terms to the left:

1/2k+7-(3k+6)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

1/2k-3k-6+7=0

We multiply all the terms by the denominator


-3k*2k-6*2k+7*2k+1=0

Wy multiply elements

-6k^2-12k+14k+1=0

We add all the numbers together, and all the variables

-6k^2+2k+1=0

a = -6; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-6)·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-6}=\frac{-2-2\sqrt{7}}{-12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-6}=\frac{-2+2\sqrt{7}}{-12}
$