4=c+5c^2

Solution for 4=c+5c^2 equation:

4=c+5c^2

We move all terms to the left:

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

We get rid of parentheses

-5c^2-c+4=0

We add all the numbers together, and all the variables

-5c^2-1c+4=0

a = -5; b = -1; c = +4;
Δ = b2-4ac
Δ = -12-4·(-5)·4
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-5}=\frac{-8}{-10}
=4/5
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-5}=\frac{10}{-10}
=-1
$