21c^2-16c-6=1-2c

Solution for 21c^2-16c-6=1-2c equation:

21c^2-16c-6=1-2c

We move all terms to the left:

21c^2-16c-6-(1-2c)=0

We add all the numbers together, and all the variables

21c^2-16c-(-2c+1)-6=0

We get rid of parentheses

21c^2-16c+2c-1-6=0

We add all the numbers together, and all the variables

21c^2-14c-7=0

a = 21; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·21·(-7)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28}{2*21}=\frac{-14}{42}
=-1/3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28}{2*21}=\frac{42}{42}
=1
$