2/5c+4/5c-6=c

Solution for 2/5c+4/5c-6=c equation:

2/5c+4/5c-6=c

We move all terms to the left:

2/5c+4/5c-6-(c)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

-1c+2/5c+4/5c-6=0

We multiply all the terms by the denominator


-1c*5c-6*5c+2+4=0

We add all the numbers together, and all the variables

-1c*5c-6*5c+6=0

Wy multiply elements

-5c^2-30c+6=0

a = -5; b = -30; c = +6;
Δ = b2-4ac
Δ = -302-4·(-5)·6
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{255}}{2*-5}=\frac{30-2\sqrt{255}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{255}}{2*-5}=\frac{30+2\sqrt{255}}{-10}
$