5/8k-4/3=-9-2/5k

Solution for 5/8k-4/3=-9-2/5k equation:

5/8k-4/3=-9-2/5k

We move all terms to the left:

5/8k-4/3-(-9-2/5k)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

5/8k-(-2/5k-9)-4/3=0

We get rid of parentheses

5/8k+2/5k+9-4/3=0

We calculate fractions


(-800k^2)/360k^2+225k/360k^2+144k/360k^2+9=0

We multiply all the terms by the denominator


(-800k^2)+225k+144k+9*360k^2=0

We add all the numbers together, and all the variables

(-800k^2)+369k+9*360k^2=0

Wy multiply elements

(-800k^2)+3240k^2+369k=0

We get rid of parentheses

-800k^2+3240k^2+369k=0

We add all the numbers together, and all the variables

2440k^2+369k=0

a = 2440; b = 369; c = 0;
Δ = b2-4ac
Δ = 3692-4·2440·0
Δ = 136161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{136161}=369$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(369)-369}{2*2440}=\frac{-738}{4880}
=-369/2440
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(369)+369}{2*2440}=\frac{0}{4880}
=0
$