1/2c-15=c

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

1/2c-15=c

We move all terms to the left:

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


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -2; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-2)·1
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{227}}{2*-2}=\frac{30-2\sqrt{227}}{-4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{227}}{2*-2}=\frac{30+2\sqrt{227}}{-4}
$