-2/7k+5/6=-1+2/3k

Solution for -2/7k+5/6=-1+2/3k equation:

-2/7k+5/6=-1+2/3k

We move all terms to the left:

-2/7k+5/6-(-1+2/3k)=0


Domain of the equation: 7k!=0

k!=0/7

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

-2/7k-(2/3k-1)+5/6=0

We get rid of parentheses

-2/7k-2/3k+1+5/6=0

We calculate fractions


315k^2/756k^2+(-216k)/756k^2+(-504k)/756k^2+1=0

We multiply all the terms by the denominator


315k^2+(-216k)+(-504k)+1*756k^2=0

Wy multiply elements

315k^2+756k^2+(-216k)+(-504k)=0

We get rid of parentheses

315k^2+756k^2-216k-504k=0

We add all the numbers together, and all the variables

1071k^2-720k=0

a = 1071; b = -720; c = 0;
Δ = b2-4ac
Δ = -7202-4·1071·0
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-720}{2*1071}=\frac{0}{2142}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+720}{2*1071}=\frac{1440}{2142}
=80/119
$