-6/7k+2/9=5-3/2k

Solution for -6/7k+2/9=5-3/2k equation:

-6/7k+2/9=5-3/2k

We move all terms to the left:

-6/7k+2/9-(5-3/2k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-6/7k-(-3/2k+5)+2/9=0

We get rid of parentheses

-6/7k+3/2k-5+2/9=0

We calculate fractions


56k^2/1134k^2+(-972k)/1134k^2+1701k/1134k^2-5=0

We multiply all the terms by the denominator


56k^2+(-972k)+1701k-5*1134k^2=0

We add all the numbers together, and all the variables

56k^2+1701k+(-972k)-5*1134k^2=0

Wy multiply elements

56k^2-5670k^2+1701k+(-972k)=0

We get rid of parentheses

56k^2-5670k^2+1701k-972k=0

We add all the numbers together, and all the variables

-5614k^2+729k=0

a = -5614; b = 729; c = 0;
Δ = b2-4ac
Δ = 7292-4·(-5614)·0
Δ = 531441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{531441}=729$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(729)-729}{2*-5614}=\frac{-1458}{-11228}
=729/5614
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(729)+729}{2*-5614}=\frac{0}{-11228}
=0
$