C(6)=20q^2-13q+6

Solution for C(6)=20q^2-13q+6 equation:

(6)=20C^2-13C+6

We move all terms to the left:

(6)-(20C^2-13C+6)=0

We get rid of parentheses

-20C^2+13C-6+6=0

We add all the numbers together, and all the variables

-20C^2+13C=0

a = -20; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-20)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-20}=\frac{-26}{-40}
=13/20
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-20}=\frac{0}{-40}
=0
$