-3/7k-8/7=6+3/4k

Solution for -3/7k-8/7=6+3/4k equation:

-3/7k-8/7=6+3/4k

We move all terms to the left:

-3/7k-8/7-(6+3/4k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-3/7k-(3/4k+6)-8/7=0

We get rid of parentheses

-3/7k-3/4k-6-8/7=0

We calculate fractions


(-12k)/1372k^2+(-1029k)/1372k^2+(-32k)/1372k^2-6=0

We multiply all the terms by the denominator


(-12k)+(-1029k)+(-32k)-6*1372k^2=0

Wy multiply elements

-8232k^2+(-12k)+(-1029k)+(-32k)=0

We get rid of parentheses

-8232k^2-12k-1029k-32k=0

We add all the numbers together, and all the variables

-8232k^2-1073k=0

a = -8232; b = -1073; c = 0;
Δ = b2-4ac
Δ = -10732-4·(-8232)·0
Δ = 1151329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1151329}=1073$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1073)-1073}{2*-8232}=\frac{0}{-16464}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1073)+1073}{2*-8232}=\frac{2146}{-16464}
=-1073/8232
$