16k-3=5/6k*10

Solution for 16k-3=5/6k*10 equation:

16k-3=5/6k*10

We move all terms to the left:

16k-3-(5/6k*10)=0


Domain of the equation: 6k*10)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

16k-(+5/6k*10)-3=0

We get rid of parentheses

16k-5/6k*10-3=0

We multiply all the terms by the denominator


16k*6k*10-3*6k*10-5=0

Wy multiply elements

960k^2*1-180k*1-5=0

Wy multiply elements

960k^2-180k-5=0

a = 960; b = -180; c = -5;
Δ = b2-4ac
Δ = -1802-4·960·(-5)
Δ = 51600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{51600}=\sqrt{400*129}=\sqrt{400}*\sqrt{129}=20\sqrt{129}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-20\sqrt{129}}{2*960}=\frac{180-20\sqrt{129}}{1920}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+20\sqrt{129}}{2*960}=\frac{180+20\sqrt{129}}{1920}
$