3/4k+7=1/8k+27

Solution for 3/4k+7=1/8k+27 equation:

3/4k+7=1/8k+27

We move all terms to the left:

3/4k+7-(1/8k+27)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 8k+27)!=0

k∈R


We get rid of parentheses

3/4k-1/8k-27+7=0

We calculate fractions


24k/32k^2+(-4k)/32k^2-27+7=0

We add all the numbers together, and all the variables

24k/32k^2+(-4k)/32k^2-20=0

We multiply all the terms by the denominator


24k+(-4k)-20*32k^2=0

Wy multiply elements

-640k^2+24k+(-4k)=0

We get rid of parentheses

-640k^2+24k-4k=0

We add all the numbers together, and all the variables

-640k^2+20k=0

a = -640; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-640)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-640}=\frac{-40}{-1280}
=1/32
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-640}=\frac{0}{-1280}
=0
$