c+5=4/9c

Solution for c+5=4/9c equation:

c+5=4/9c

We move all terms to the left:

c+5-(4/9c)=0


Domain of the equation: 9c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

c-(+4/9c)+5=0

We get rid of parentheses

c-4/9c+5=0

We multiply all the terms by the denominator


c*9c+5*9c-4=0

Wy multiply elements

9c^2+45c-4=0

a = 9; b = 45; c = -4;
Δ = b2-4ac
Δ = 452-4·9·(-4)
Δ = 2169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{241}}{2*9}=\frac{-45-3\sqrt{241}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{241}}{2*9}=\frac{-45+3\sqrt{241}}{18}
$