6+4/5c=9/10c

Solution for 6+4/5c=9/10c equation:

6+4/5c=9/10c

We move all terms to the left:

6+4/5c-(9/10c)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R



Domain of the equation: 10c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

4/5c-(+9/10c)+6=0

We get rid of parentheses

4/5c-9/10c+6=0

We calculate fractions


40c/50c^2+(-45c)/50c^2+6=0

We multiply all the terms by the denominator


40c+(-45c)+6*50c^2=0

Wy multiply elements

300c^2+40c+(-45c)=0

We get rid of parentheses

300c^2+40c-45c=0

We add all the numbers together, and all the variables

300c^2-5c=0

a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600}
=1/60
$