5/9k+2/7=5+5/8k

Solution for 5/9k+2/7=5+5/8k equation:

5/9k+2/7=5+5/8k

We move all terms to the left:

5/9k+2/7-(5+5/8k)=0


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 8k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

5/9k-(5/8k+5)+2/7=0

We get rid of parentheses

5/9k-5/8k-5+2/7=0

We calculate fractions


1152k^2/3528k^2+1960k/3528k^2+(-2205k)/3528k^2-5=0

We multiply all the terms by the denominator


1152k^2+1960k+(-2205k)-5*3528k^2=0

Wy multiply elements

1152k^2-17640k^2+1960k+(-2205k)=0

We get rid of parentheses

1152k^2-17640k^2+1960k-2205k=0

We add all the numbers together, and all the variables

-16488k^2-245k=0

a = -16488; b = -245; c = 0;
Δ = b2-4ac
Δ = -2452-4·(-16488)·0
Δ = 60025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{60025}=245$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-245)-245}{2*-16488}=\frac{0}{-32976}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+245}{2*-16488}=\frac{490}{-32976}
=-245/16488
$