8/9c+1/3c=1/4

Solution for 8/9c+1/3c=1/4 equation:

8/9c+1/3c=1/4

We move all terms to the left:

8/9c+1/3c-(1/4)=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

8/9c+1/3c-(+1/4)=0

We get rid of parentheses

8/9c+1/3c-1/4=0

We calculate fractions


(-81c^2)/432c^2+384c/432c^2+144c/432c^2=0

We multiply all the terms by the denominator


(-81c^2)+384c+144c=0

We add all the numbers together, and all the variables

(-81c^2)+528c=0

We get rid of parentheses

-81c^2+528c=0

a = -81; b = 528; c = 0;
Δ = b2-4ac
Δ = 5282-4·(-81)·0
Δ = 278784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{278784}=528$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(528)-528}{2*-81}=\frac{-1056}{-162}
=6+14/27
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(528)+528}{2*-81}=\frac{0}{-162}
=0
$