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

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

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

We move all terms to the left:

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


Domain of the equation: 4k!=0

k!=0/4

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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-32k^2)/648k^2+1458k/648k^2+2916k/648k^2+4=0

We multiply all the terms by the denominator


(-32k^2)+1458k+2916k+4*648k^2=0

We add all the numbers together, and all the variables

(-32k^2)+4374k+4*648k^2=0

Wy multiply elements

(-32k^2)+2592k^2+4374k=0

We get rid of parentheses

-32k^2+2592k^2+4374k=0

We add all the numbers together, and all the variables

2560k^2+4374k=0

a = 2560; b = 4374; c = 0;
Δ = b2-4ac
Δ = 43742-4·2560·0
Δ = 19131876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19131876}=4374$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4374)-4374}{2*2560}=\frac{-8748}{5120}
=-1+907/1280
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4374)+4374}{2*2560}=\frac{0}{5120}
=0
$