-8/3k-6/5=-4+6/7k

Solution for -8/3k-6/5=-4+6/7k equation:

-8/3k-6/5=-4+6/7k

We move all terms to the left:

-8/3k-6/5-(-4+6/7k)=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-(6/7k-4)-6/5=0

We get rid of parentheses

-8/3k-6/7k+4-6/5=0

We calculate fractions


(-882k^2)/525k^2+(-1400k)/525k^2+(-450k)/525k^2+4=0

We multiply all the terms by the denominator


(-882k^2)+(-1400k)+(-450k)+4*525k^2=0

Wy multiply elements

(-882k^2)+2100k^2+(-1400k)+(-450k)=0

We get rid of parentheses

-882k^2+2100k^2-1400k-450k=0

We add all the numbers together, and all the variables

1218k^2-1850k=0

a = 1218; b = -1850; c = 0;
Δ = b2-4ac
Δ = -18502-4·1218·0
Δ = 3422500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3422500}=1850$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1850)-1850}{2*1218}=\frac{0}{2436}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1850)+1850}{2*1218}=\frac{3700}{2436}
=1+316/609
$