8/c-2=2c-12

Solution for 8/c-2=2c-12 equation:

8/c-2=2c-12

We move all terms to the left:

8/c-2-(2c-12)=0


Domain of the equation: c!=0

c∈R


We get rid of parentheses

8/c-2c+12-2=0

We multiply all the terms by the denominator


-2c*c+12*c-2*c+8=0

We add all the numbers together, and all the variables

10c-2c*c+8=0

Wy multiply elements

-2c^2+10c+8=0

a = -2; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·(-2)·8
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{41}}{2*-2}=\frac{-10-2\sqrt{41}}{-4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{41}}{2*-2}=\frac{-10+2\sqrt{41}}{-4}
$