3/5c-2=1/2c+3

Solution for 3/5c-2=1/2c+3 equation:

3/5c-2=1/2c+3

We move all terms to the left:

3/5c-2-(1/2c+3)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R



Domain of the equation: 2c+3)!=0

c∈R


We get rid of parentheses

3/5c-1/2c-3-2=0

We calculate fractions


6c/10c^2+(-5c)/10c^2-3-2=0

We add all the numbers together, and all the variables

6c/10c^2+(-5c)/10c^2-5=0

We multiply all the terms by the denominator


6c+(-5c)-5*10c^2=0

Wy multiply elements

-50c^2+6c+(-5c)=0

We get rid of parentheses

-50c^2+6c-5c=0

We add all the numbers together, and all the variables

-50c^2+c=0

a = -50; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-50)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-50}=\frac{-2}{-100}
=1/50
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-50}=\frac{0}{-100}
=0
$