2c(c+1)=11c+81

Solution for 2c(c+1)=11c+81 equation:

2c(c+1)=11c+81

We move all terms to the left:

2c(c+1)-(11c+81)=0

We multiply parentheses

2c^2+2c-(11c+81)=0

We get rid of parentheses

2c^2+2c-11c-81=0

We add all the numbers together, and all the variables

2c^2-9c-81=0

a = 2; b = -9; c = -81;
Δ = b2-4ac
Δ = -92-4·2·(-81)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-27}{2*2}=\frac{-18}{4}
=-4+1/2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+27}{2*2}=\frac{36}{4}
=9
$