(7/12*c+1)=c

Solution for (7/12*c+1)=c equation:

(7/12c+1)=c

We move all terms to the left:

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


Domain of the equation: 12c+1)!=0

c∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1c*12c+1*12c+7=0

Wy multiply elements

-12c^2+12c+7=0

a = -12; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-12)·7
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{30}}{2*-12}=\frac{-12-4\sqrt{30}}{-24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{30}}{2*-12}=\frac{-12+4\sqrt{30}}{-24}
$