5/2c-3=3/7c+3

Solution for 5/2c-3=3/7c+3 equation:

5/2c-3=3/7c+3

We move all terms to the left:

5/2c-3-(3/7c+3)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R



Domain of the equation: 7c+3)!=0

c∈R


We get rid of parentheses

5/2c-3/7c-3-3=0

We calculate fractions


35c/14c^2+(-6c)/14c^2-3-3=0

We add all the numbers together, and all the variables

35c/14c^2+(-6c)/14c^2-6=0

We multiply all the terms by the denominator


35c+(-6c)-6*14c^2=0

Wy multiply elements

-84c^2+35c+(-6c)=0

We get rid of parentheses

-84c^2+35c-6c=0

We add all the numbers together, and all the variables

-84c^2+29c=0

a = -84; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-84)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-84}=\frac{-58}{-168}
=29/84
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-84}=\frac{0}{-168}
=0
$