7/4k-9/2=-1+7/9k

Solution for 7/4k-9/2=-1+7/9k equation:

7/4k-9/2=-1+7/9k

We move all terms to the left:

7/4k-9/2-(-1+7/9k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 9k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

7/4k-(7/9k-1)-9/2=0

We get rid of parentheses

7/4k-7/9k+1-9/2=0

We calculate fractions


(-2916k^2)/144k^2+252k/144k^2+(-112k)/144k^2+1=0

We multiply all the terms by the denominator


(-2916k^2)+252k+(-112k)+1*144k^2=0

Wy multiply elements

(-2916k^2)+144k^2+252k+(-112k)=0

We get rid of parentheses

-2916k^2+144k^2+252k-112k=0

We add all the numbers together, and all the variables

-2772k^2+140k=0

a = -2772; b = 140; c = 0;
Δ = b2-4ac
Δ = 1402-4·(-2772)·0
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-140}{2*-2772}=\frac{-280}{-5544}
=5/99
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+140}{2*-2772}=\frac{0}{-5544}
=0
$