-5/2k+2/3=4-2/5k

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

-5/2k+2/3=4-2/5k

We move all terms to the left:

-5/2k+2/3-(4-2/5k)=0


Domain of the equation: 2k!=0

k!=0/2

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

-5/2k-(-2/5k+4)+2/3=0

We get rid of parentheses

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

We calculate fractions


100k^2/90k^2+(-225k)/90k^2+36k/90k^2-4=0

We multiply all the terms by the denominator


100k^2+(-225k)+36k-4*90k^2=0

We add all the numbers together, and all the variables

100k^2+36k+(-225k)-4*90k^2=0

Wy multiply elements

100k^2-360k^2+36k+(-225k)=0

We get rid of parentheses

100k^2-360k^2+36k-225k=0

We add all the numbers together, and all the variables

-260k^2-189k=0

a = -260; b = -189; c = 0;
Δ = b2-4ac
Δ = -1892-4·(-260)·0
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-189}{2*-260}=\frac{0}{-520}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+189}{2*-260}=\frac{378}{-520}
=-189/260
$