1/4c-3(1/2c+3)=-3/4c

Solution for 1/4c-3(1/2c+3)=-3/4c equation:

1/4c-3(1/2c+3)=-3/4c

We move all terms to the left:

1/4c-3(1/2c+3)-(-3/4c)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 2c+3)!=0

c∈R



Domain of the equation: 4c)!=0

c!=0/1

c!=0

c∈R


We multiply parentheses

1/4c-3c-(-3/4c)-9=0

We get rid of parentheses

1/4c-3c+3/4c-9=0

We multiply all the terms by the denominator


-3c*4c-9*4c+1+3=0

We add all the numbers together, and all the variables

-3c*4c-9*4c+4=0

Wy multiply elements

-12c^2-36c+4=0

a = -12; b = -36; c = +4;
Δ = b2-4ac
Δ = -362-4·(-12)·4
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{93}}{2*-12}=\frac{36-4\sqrt{93}}{-24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{93}}{2*-12}=\frac{36+4\sqrt{93}}{-24}
$