5/9c-3/4=3/7c

Solution for 5/9c-3/4=3/7c equation:

5/9c-3/4=3/7c

We move all terms to the left:

5/9c-3/4-(3/7c)=0


Domain of the equation: 9c!=0

c!=0/9

c!=0

c∈R



Domain of the equation: 7c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

5/9c-(+3/7c)-3/4=0

We get rid of parentheses

5/9c-3/7c-3/4=0

We calculate fractions


(-1323c^2)/1008c^2+560c/1008c^2+(-432c)/1008c^2=0

We multiply all the terms by the denominator


(-1323c^2)+560c+(-432c)=0

We get rid of parentheses

-1323c^2+560c-432c=0

We add all the numbers together, and all the variables

-1323c^2+128c=0

a = -1323; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·(-1323)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*-1323}=\frac{-256}{-2646}
=128/1323
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*-1323}=\frac{0}{-2646}
=0
$