1/2c-3=2c-24

Solution for 1/2c-3=2c-24 equation:

1/2c-3=2c-24

We move all terms to the left:

1/2c-3-(2c-24)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We get rid of parentheses

1/2c-2c+24-3=0

We multiply all the terms by the denominator


-2c*2c+24*2c-3*2c+1=0

Wy multiply elements

-4c^2+48c-6c+1=0

We add all the numbers together, and all the variables

-4c^2+42c+1=0

a = -4; b = 42; c = +1;
Δ = b2-4ac
Δ = 422-4·(-4)·1
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{445}}{2*-4}=\frac{-42-2\sqrt{445}}{-8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{445}}{2*-4}=\frac{-42+2\sqrt{445}}{-8}
$