3+3/2k=4k-2

Solution for 3+3/2k=4k-2 equation:

3+3/2k=4k-2

We move all terms to the left:

3+3/2k-(4k-2)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

3/2k-4k+2+3=0

We multiply all the terms by the denominator


-4k*2k+2*2k+3*2k+3=0

Wy multiply elements

-8k^2+4k+6k+3=0

We add all the numbers together, and all the variables

-8k^2+10k+3=0

a = -8; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-8)·3
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-8}=\frac{4}{-16}
=-1/4
$