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

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

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

We move all terms to the left:

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


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: c!=0

c∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


3c+(-4c)-4*4c^2=0

Wy multiply elements

-16c^2+3c+(-4c)=0

We get rid of parentheses

-16c^2+3c-4c=0

We add all the numbers together, and all the variables

-16c^2-1c=0

a = -16; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-16)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-16}=\frac{0}{-32}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-16}=\frac{2}{-32}
=-1/16
$