-3/8k-2/7=-5+1/3k

Solution for -3/8k-2/7=-5+1/3k equation:

-3/8k-2/7=-5+1/3k

We move all terms to the left:

-3/8k-2/7-(-5+1/3k)=0


Domain of the equation: 8k!=0

k!=0/8

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

-3/8k-(1/3k-5)-2/7=0

We get rid of parentheses

-3/8k-1/3k+5-2/7=0

We calculate fractions


(-144k^2)/1176k^2+(-441k)/1176k^2+(-392k)/1176k^2+5=0

We multiply all the terms by the denominator


(-144k^2)+(-441k)+(-392k)+5*1176k^2=0

Wy multiply elements

(-144k^2)+5880k^2+(-441k)+(-392k)=0

We get rid of parentheses

-144k^2+5880k^2-441k-392k=0

We add all the numbers together, and all the variables

5736k^2-833k=0

a = 5736; b = -833; c = 0;
Δ = b2-4ac
Δ = -8332-4·5736·0
Δ = 693889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{693889}=833$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-833)-833}{2*5736}=\frac{0}{11472}
=0$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-833)+833}{2*5736}=\frac{1666}{11472}
=833/5736$