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

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

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

We move all terms to the left:

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


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


81k/135k^2+10k/135k^2+25k/135k^2-5=0

We multiply all the terms by the denominator


81k+10k+25k-5*135k^2=0

We add all the numbers together, and all the variables

116k-5*135k^2=0

Wy multiply elements

-675k^2+116k=0

a = -675; b = 116; c = 0;
Δ = b2-4ac
Δ = 1162-4·(-675)·0
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-116}{2*-675}=\frac{-232}{-1350}
=116/675
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+116}{2*-675}=\frac{0}{-1350}
=0
$