3c+4/c-6=c+6

Solution for 3c+4/c-6=c+6 equation:

3c+4/c-6=c+6

We move all terms to the left:

3c+4/c-6-(c+6)=0


Domain of the equation: c!=0

c∈R


We get rid of parentheses

3c+4/c-c-6-6=0

We multiply all the terms by the denominator


3c*c-c*c-6*c-6*c+4=0

We add all the numbers together, and all the variables

-12c+3c*c-c*c+4=0

Wy multiply elements

3c^2-1c^2-12c+4=0

We add all the numbers together, and all the variables

2c^2-12c+4=0

a = 2; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·2·4
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{7}}{2*2}=\frac{12-4\sqrt{7}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{7}}{2*2}=\frac{12+4\sqrt{7}}{4}
$