4/2k+5=2-3/k+2

Solution for 4/2k+5=2-3/k+2 equation:

4/2k+5=2-3/k+2

We move all terms to the left:

4/2k+5-(2-3/k+2)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: k+2)!=0

k∈R


We add all the numbers together, and all the variables

4/2k-(-3/k+4)+5=0

We get rid of parentheses

4/2k+3/k-4+5=0

We calculate fractions


4k/2k^2+6k/2k^2-4+5=0

We add all the numbers together, and all the variables

4k/2k^2+6k/2k^2+1=0

We multiply all the terms by the denominator


4k+6k+1*2k^2=0

We add all the numbers together, and all the variables

10k+1*2k^2=0

Wy multiply elements

2k^2+10k=0

a = 2; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·2·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*2}=\frac{-20}{4}
=-5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*2}=\frac{0}{4}
=0
$