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)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 8k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

224k^2+24k+(-4k)=0

We get rid of parentheses

224k^2+24k-4k=0

We add all the numbers together, and all the variables

224k^2+20k=0

a = 224; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·224·0
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*224}=\frac{-40}{448}
=-5/56
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*224}=\frac{0}{448}
=0
$