-2/9k+9/8=-49/2k

Solution for -2/9k+9/8=-49/2k equation:

-2/9k+9/8=-49/2k

We move all terms to the left:

-2/9k+9/8-(-49/2k)=0


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We get rid of parentheses

-2/9k+49/2k+9/8=0

We calculate fractions


324k^2/1152k^2+(-256k)/1152k^2+28224k/1152k^2=0

We multiply all the terms by the denominator


324k^2+(-256k)+28224k=0

We add all the numbers together, and all the variables

324k^2+28224k+(-256k)=0

We get rid of parentheses

324k^2+28224k-256k=0

We add all the numbers together, and all the variables

324k^2+27968k=0

a = 324; b = 27968; c = 0;
Δ = b2-4ac
Δ = 279682-4·324·0
Δ = 782209024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{782209024}=27968$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27968)-27968}{2*324}=\frac{-55936}{648}
=-86+26/81
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27968)+27968}{2*324}=\frac{0}{648}
=0
$