7/8k-4/5=7+1/9k

Solution for 7/8k-4/5=7+1/9k equation:

7/8k-4/5=7+1/9k

We move all terms to the left:

7/8k-4/5-(7+1/9k)=0


Domain of the equation: 8k!=0

k!=0/8

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

7/8k-(1/9k+7)-4/5=0

We get rid of parentheses

7/8k-1/9k-7-4/5=0

We calculate fractions


(-2592k^2)/1800k^2+1575k/1800k^2+(-200k)/1800k^2-7=0

We multiply all the terms by the denominator


(-2592k^2)+1575k+(-200k)-7*1800k^2=0

Wy multiply elements

(-2592k^2)-12600k^2+1575k+(-200k)=0

We get rid of parentheses

-2592k^2-12600k^2+1575k-200k=0

We add all the numbers together, and all the variables

-15192k^2+1375k=0

a = -15192; b = 1375; c = 0;
Δ = b2-4ac
Δ = 13752-4·(-15192)·0
Δ = 1890625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1890625}=1375$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1375)-1375}{2*-15192}=\frac{-2750}{-30384}
=1375/15192
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1375)+1375}{2*-15192}=\frac{0}{-30384}
=0
$