1/4k+2=1/2k-3

Solution for 1/4k+2=1/2k-3 equation:

1/4k+2=1/2k-3

We move all terms to the left:

1/4k+2-(1/2k-3)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 2k-3)!=0

k∈R


We get rid of parentheses

1/4k-1/2k+3+2=0

We calculate fractions


2k/8k^2+(-4k)/8k^2+3+2=0

We add all the numbers together, and all the variables

2k/8k^2+(-4k)/8k^2+5=0

We multiply all the terms by the denominator


2k+(-4k)+5*8k^2=0

Wy multiply elements

40k^2+2k+(-4k)=0

We get rid of parentheses

40k^2+2k-4k=0

We add all the numbers together, and all the variables

40k^2-2k=0

a = 40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·40·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*40}=\frac{0}{80}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*40}=\frac{4}{80}
=1/20
$