1/2c-15=c+6

Solution for 1/2c-15=c+6 equation:

1/2c-15=c+6

We move all terms to the left:

1/2c-15-(c+6)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We get rid of parentheses

1/2c-c-6-15=0

We multiply all the terms by the denominator


-c*2c-6*2c-15*2c+1=0

Wy multiply elements

-2c^2-12c-30c+1=0

We add all the numbers together, and all the variables

-2c^2-42c+1=0

a = -2; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·(-2)·1
Δ = 1772
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:

$\sqrt{\Delta}=\sqrt{1772}=\sqrt{4*443}=\sqrt{4}*\sqrt{443}=2\sqrt{443}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{443}}{2*-2}=\frac{42-2\sqrt{443}}{-4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{443}}{2*-2}=\frac{42+2\sqrt{443}}{-4}
$