-6/5k+2/9=-9+2/3k

Solution for -6/5k+2/9=-9+2/3k equation:

-6/5k+2/9=-9+2/3k

We move all terms to the left:

-6/5k+2/9-(-9+2/3k)=0


Domain of the equation: 5k!=0

k!=0/5

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

-6/5k-(2/3k-9)+2/9=0

We get rid of parentheses

-6/5k-2/3k+9+2/9=0

We calculate fractions


90k^2/1215k^2+(-1458k)/1215k^2+(-810k)/1215k^2+9=0

We multiply all the terms by the denominator


90k^2+(-1458k)+(-810k)+9*1215k^2=0

Wy multiply elements

90k^2+10935k^2+(-1458k)+(-810k)=0

We get rid of parentheses

90k^2+10935k^2-1458k-810k=0

We add all the numbers together, and all the variables

11025k^2-2268k=0

a = 11025; b = -2268; c = 0;
Δ = b2-4ac
Δ = -22682-4·11025·0
Δ = 5143824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5143824}=2268$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2268)-2268}{2*11025}=\frac{0}{22050}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2268)+2268}{2*11025}=\frac{4536}{22050}
=36/175
$