c+c(11/3)+5.50=26.50

Solution for c+c(11/3)+5.50=26.50 equation:

c+c(11/3)+5.50=26.50

We move all terms to the left:

c+c(11/3)+5.50-(26.50)=0

We add all the numbers together, and all the variables

c+c(+11/3)+5.50-(26.5)=0

We add all the numbers together, and all the variables

c+c(+11/3)-21=0

We multiply parentheses

11c^2+c-21=0

a = 11; b = 1; c = -21;
Δ = b2-4ac
Δ = 12-4·11·(-21)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{37}}{2*11}=\frac{-1-5\sqrt{37}}{22}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{37}}{2*11}=\frac{-1+5\sqrt{37}}{22}
$