4/3c-17-5/9c=11

Solution for 4/3c-17-5/9c=11 equation:

4/3c-17-5/9c=11

We move all terms to the left:

4/3c-17-5/9c-(11)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R



Domain of the equation: 9c!=0

c!=0/9

c!=0

c∈R


We add all the numbers together, and all the variables

4/3c-5/9c-28=0

We calculate fractions


36c/27c^2+(-15c)/27c^2-28=0

We multiply all the terms by the denominator


36c+(-15c)-28*27c^2=0

Wy multiply elements

-756c^2+36c+(-15c)=0

We get rid of parentheses

-756c^2+36c-15c=0

We add all the numbers together, and all the variables

-756c^2+21c=0

a = -756; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-756)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-756}=\frac{-42}{-1512}
=1/36
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-756}=\frac{0}{-1512}
=0
$