24/c=12-c

Solution for 24/c=12-c equation:

24/c=12-c

We move all terms to the left:

24/c-(12-c)=0


Domain of the equation: c!=0

c∈R


We add all the numbers together, and all the variables

24/c-(-1c+12)=0

We get rid of parentheses

24/c+1c-12=0

We multiply all the terms by the denominator


1c*c-12*c+24=0

We add all the numbers together, and all the variables

-12c+1c*c+24=0

Wy multiply elements

c^2-12c+24=0

a = 1; b = -12; c = +24;
Δ = b2-4ac
Δ = -122-4·1·24
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*1}=\frac{12-4\sqrt{3}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*1}=\frac{12+4\sqrt{3}}{2}
$