5/7c+1/3-2=-9/21c

Solution for 5/7c+1/3-2=-9/21c equation:

5/7c+1/3-2=-9/21c

We move all terms to the left:

5/7c+1/3-2-(-9/21c)=0


Domain of the equation: 7c!=0

c!=0/7

c!=0

c∈R



Domain of the equation: 21c)!=0

c!=0/1

c!=0

c∈R


We get rid of parentheses

5/7c+9/21c-2+1/3=0

We calculate fractions


294c^2/1323c^2+945c/1323c^2+567c/1323c^2-2=0

We multiply all the terms by the denominator


294c^2+945c+567c-2*1323c^2=0

We add all the numbers together, and all the variables

294c^2+1512c-2*1323c^2=0

Wy multiply elements

294c^2-2646c^2+1512c=0

We add all the numbers together, and all the variables

-2352c^2+1512c=0

a = -2352; b = 1512; c = 0;
Δ = b2-4ac
Δ = 15122-4·(-2352)·0
Δ = 2286144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2286144}=1512$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1512)-1512}{2*-2352}=\frac{-3024}{-4704}
=9/14
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1512)+1512}{2*-2352}=\frac{0}{-4704}
=0
$