3/4c+1/5c=2/9

Solution for 3/4c+1/5c=2/9 equation:

3/4c+1/5c=2/9

We move all terms to the left:

3/4c+1/5c-(2/9)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

3/4c+1/5c-(+2/9)=0

We get rid of parentheses

3/4c+1/5c-2/9=0

We calculate fractions


(-200c^2)/1620c^2+1215c/1620c^2+324c/1620c^2=0

We multiply all the terms by the denominator


(-200c^2)+1215c+324c=0

We add all the numbers together, and all the variables

(-200c^2)+1539c=0

We get rid of parentheses

-200c^2+1539c=0

a = -200; b = 1539; c = 0;
Δ = b2-4ac
Δ = 15392-4·(-200)·0
Δ = 2368521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2368521}=1539$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1539)-1539}{2*-200}=\frac{-3078}{-400}
=7+139/200
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1539)+1539}{2*-200}=\frac{0}{-400}
=0
$