2(1-8c)=5-3(6c+1)4c

Solution for 2(1-8c)=5-3(6c+1)4c equation:

2(1-8c)=5-3(6c+1)4c

We move all terms to the left:

2(1-8c)-(5-3(6c+1)4c)=0

We add all the numbers together, and all the variables

2(-8c+1)-(5-3(6c+1)4c)=0

We multiply parentheses

-16c-(5-3(6c+1)4c)+2=0


We calculate terms in parentheses: -(5-3(6c+1)4c), so:

5-3(6c+1)4c

determiningTheFunctionDomain
-3(6c+1)4c+5

We multiply parentheses

-72c^2-12c+5

Back to the equation:

-(-72c^2-12c+5)


We get rid of parentheses

72c^2+12c-16c-5+2=0

We add all the numbers together, and all the variables

72c^2-4c-3=0

a = 72; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·72·(-3)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{55}}{2*72}=\frac{4-4\sqrt{55}}{144}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{55}}{2*72}=\frac{4+4\sqrt{55}}{144}
$