5/6c-2/3c=1

Solution for 5/6c-2/3c=1 equation:

5/6c-2/3c=1

We move all terms to the left:

5/6c-2/3c-(1)=0


Domain of the equation: 6c!=0

c!=0/6

c!=0

c∈R



Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We calculate fractions


15c/18c^2+(-12c)/18c^2-1=0

We multiply all the terms by the denominator


15c+(-12c)-1*18c^2=0

Wy multiply elements

-18c^2+15c+(-12c)=0

We get rid of parentheses

-18c^2+15c-12c=0

We add all the numbers together, and all the variables

-18c^2+3c=0

a = -18; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-18)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-18}=\frac{-6}{-36}
=1/6
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-18}=\frac{0}{-36}
=0
$