-6/5k+9/8=1-1/6k

Solution for -6/5k+9/8=1-1/6k equation:

-6/5k+9/8=1-1/6k

We move all terms to the left:

-6/5k+9/8-(1-1/6k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-6/5k-(-1/6k+1)+9/8=0

We get rid of parentheses

-6/5k+1/6k-1+9/8=0

We calculate fractions


1620k^2/1920k^2+(-2304k)/1920k^2+320k/1920k^2-1=0

We multiply all the terms by the denominator


1620k^2+(-2304k)+320k-1*1920k^2=0

We add all the numbers together, and all the variables

1620k^2+320k+(-2304k)-1*1920k^2=0

Wy multiply elements

1620k^2-1920k^2+320k+(-2304k)=0

We get rid of parentheses

1620k^2-1920k^2+320k-2304k=0

We add all the numbers together, and all the variables

-300k^2-1984k=0

a = -300; b = -1984; c = 0;
Δ = b2-4ac
Δ = -19842-4·(-300)·0
Δ = 3936256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3936256}=1984$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1984)-1984}{2*-300}=\frac{0}{-600}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1984)+1984}{2*-300}=\frac{3968}{-600}
=-6+46/75
$