6+4/5k=9/10k

Solution for 6+4/5k=9/10k equation:

6+4/5k=9/10k

We move all terms to the left:

6+4/5k-(9/10k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 10k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

4/5k-(+9/10k)+6=0

We get rid of parentheses

4/5k-9/10k+6=0

We calculate fractions


40k/50k^2+(-45k)/50k^2+6=0

We multiply all the terms by the denominator


40k+(-45k)+6*50k^2=0

Wy multiply elements

300k^2+40k+(-45k)=0

We get rid of parentheses

300k^2+40k-45k=0

We add all the numbers together, and all the variables

300k^2-5k=0

a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600}
=1/60
$