-4/9k-9/2=-4+2/7k

Solution for -4/9k-9/2=-4+2/7k equation:

-4/9k-9/2=-4+2/7k

We move all terms to the left:

-4/9k-9/2-(-4+2/7k)=0


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-4/9k-(2/7k-4)-9/2=0

We get rid of parentheses

-4/9k-2/7k+4-9/2=0

We calculate fractions


(-3969k^2)/252k^2+(-112k)/252k^2+(-72k)/252k^2+4=0

We multiply all the terms by the denominator


(-3969k^2)+(-112k)+(-72k)+4*252k^2=0

Wy multiply elements

(-3969k^2)+1008k^2+(-112k)+(-72k)=0

We get rid of parentheses

-3969k^2+1008k^2-112k-72k=0

We add all the numbers together, and all the variables

-2961k^2-184k=0

a = -2961; b = -184; c = 0;
Δ = b2-4ac
Δ = -1842-4·(-2961)·0
Δ = 33856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33856}=184$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-184}{2*-2961}=\frac{0}{-5922}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+184}{2*-2961}=\frac{368}{-5922}
=-184/2961
$