(8)/(3)k+(3)/(5)=-6-(9)/(7)k

Solution for (8)/(3)k+(3)/(5)=-6-(9)/(7)k equation:

(8)/(3)k+(3)/(5)=-6-(9)/(7)k

We move all terms to the left:

(8)/(3)k+(3)/(5)-(-6-(9)/(7)k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

8/3k-(-9/7k-6)+3/5=0

We get rid of parentheses

8/3k+9/7k+6+3/5=0

We calculate fractions


441k^2/525k^2+1400k/525k^2+675k/525k^2+6=0

We multiply all the terms by the denominator


441k^2+1400k+675k+6*525k^2=0

We add all the numbers together, and all the variables

441k^2+2075k+6*525k^2=0

Wy multiply elements

441k^2+3150k^2+2075k=0

We add all the numbers together, and all the variables

3591k^2+2075k=0

a = 3591; b = 2075; c = 0;
Δ = b2-4ac
Δ = 20752-4·3591·0
Δ = 4305625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4305625}=2075$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2075)-2075}{2*3591}=\frac{-4150}{7182}
=-2075/3591
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2075)+2075}{2*3591}=\frac{0}{7182}
=0
$