5/9c+1/3c=1/8

Solution for 5/9c+1/3c=1/8 equation:

5/9c+1/3c=1/8

We move all terms to the left:

5/9c+1/3c-(1/8)=0


Domain of the equation: 9c!=0

c!=0/9

c!=0

c∈R



Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We add all the numbers together, and all the variables

5/9c+1/3c-(+1/8)=0

We get rid of parentheses

5/9c+1/3c-1/8=0

We calculate fractions


(-81c^2)/1728c^2+960c/1728c^2+576c/1728c^2=0

We multiply all the terms by the denominator


(-81c^2)+960c+576c=0

We add all the numbers together, and all the variables

(-81c^2)+1536c=0

We get rid of parentheses

-81c^2+1536c=0

a = -81; b = 1536; c = 0;
Δ = b2-4ac
Δ = 15362-4·(-81)·0
Δ = 2359296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2359296}=1536$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1536)-1536}{2*-81}=\frac{-3072}{-162}
=18+26/27
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1536)+1536}{2*-81}=\frac{0}{-162}
=0
$