1/2k-5=1/4k+7

Solution for 1/2k-5=1/4k+7 equation:

1/2k-5=1/4k+7

We move all terms to the left:

1/2k-5-(1/4k+7)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 4k+7)!=0

k∈R


We get rid of parentheses

1/2k-1/4k-7-5=0

We calculate fractions


4k/8k^2+(-2k)/8k^2-7-5=0

We add all the numbers together, and all the variables

4k/8k^2+(-2k)/8k^2-12=0

We multiply all the terms by the denominator


4k+(-2k)-12*8k^2=0

Wy multiply elements

-96k^2+4k+(-2k)=0

We get rid of parentheses

-96k^2+4k-2k=0

We add all the numbers together, and all the variables

-96k^2+2k=0

a = -96; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-96)·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*-96}=\frac{-4}{-192}
=1/48
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-96}=\frac{0}{-192}
=0
$