3/4c+1/4+3=7+3/12c

Solution for 3/4c+1/4+3=7+3/12c equation:

3/4c+1/4+3=7+3/12c

We move all terms to the left:

3/4c+1/4+3-(7+3/12c)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 12c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

3/4c-(3/12c+7)+3+1/4=0

We get rid of parentheses

3/4c-3/12c-7+3+1/4=0

We calculate fractions


36c/768c^2+(-192c)/768c^2+12c/768c^2-7+3=0

We add all the numbers together, and all the variables

36c/768c^2+(-192c)/768c^2+12c/768c^2-4=0

We multiply all the terms by the denominator


36c+(-192c)+12c-4*768c^2=0

We add all the numbers together, and all the variables

48c+(-192c)-4*768c^2=0

Wy multiply elements

-3072c^2+48c+(-192c)=0

We get rid of parentheses

-3072c^2+48c-192c=0

We add all the numbers together, and all the variables

-3072c^2-144c=0

a = -3072; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-3072)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-3072}=\frac{0}{-6144}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-3072}=\frac{288}{-6144}
=-3/64
$