3/c=4-c

Solution for 3/c=4-c equation:

3/c=4-c

We move all terms to the left:

3/c-(4-c)=0


Domain of the equation: c!=0

c∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/c+1c-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

c^2-4c+3=0

a = 1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*1}=\frac{2}{2}
=1
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*1}=\frac{6}{2}
=3
$