c+c2+2=5c-1

Solution for c+c2+2=5c-1 equation:

c+c2+2=5c-1

We move all terms to the left:

c+c2+2-(5c-1)=0

We add all the numbers together, and all the variables

c^2+c-(5c-1)+2=0

We get rid of parentheses

c^2+c-5c+1+2=0

We add all the numbers together, and all the variables

c^2-4c+3=0

a = 1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*1}=\frac{2}{2}
=1$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*1}=\frac{6}{2}
=3$