2/5c=16c

Solution for 2/5c=16c equation:

2/5c=16c

We move all terms to the left:

2/5c-(16c)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

-16c+2/5c=0

We multiply all the terms by the denominator


-16c*5c+2=0

Wy multiply elements

-80c^2+2=0

a = -80; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-80)·2
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-80}=\frac{0-8\sqrt{10}}{-160}
=-\frac{8\sqrt{10}}{-160}
=-\frac{\sqrt{10}}{-20}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-80}=\frac{0+8\sqrt{10}}{-160}
=\frac{8\sqrt{10}}{-160}
=\frac{\sqrt{10}}{-20}
$