11/5c=c+1

Solution for 11/5c=c+1 equation:

11/5c=c+1

We move all terms to the left:

11/5c-(c+1)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We get rid of parentheses

11/5c-c-1=0

We multiply all the terms by the denominator


-c*5c-1*5c+11=0

Wy multiply elements

-5c^2-5c+11=0

a = -5; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-5)·11
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7\sqrt{5}}{2*-5}=\frac{5-7\sqrt{5}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7\sqrt{5}}{2*-5}=\frac{5+7\sqrt{5}}{-10}
$