3-2/9c=1/3c-7

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

3-2/9c=1/3c-7

We move all terms to the left:

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


Domain of the equation: 9c!=0

c!=0/9

c!=0

c∈R



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

c∈R


We get rid of parentheses

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

We calculate fractions


(-6c)/27c^2+(-9c)/27c^2+7+3=0

We add all the numbers together, and all the variables

(-6c)/27c^2+(-9c)/27c^2+10=0

We multiply all the terms by the denominator


(-6c)+(-9c)+10*27c^2=0

Wy multiply elements

270c^2+(-6c)+(-9c)=0

We get rid of parentheses

270c^2-6c-9c=0

We add all the numbers together, and all the variables

270c^2-15c=0

a = 270; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·270·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*270}=\frac{0}{540}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*270}=\frac{30}{540}
=1/18
$