1/2c+1/3c=2+3

Solution for 1/2c+1/3c=2+3 equation:

1/2c+1/3c=2+3

We move all terms to the left:

1/2c+1/3c-(2+3)=0


Domain of the equation: 2c!=0

c!=0/2

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

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

We calculate fractions


3c/6c^2+2c/6c^2-5=0

We multiply all the terms by the denominator


3c+2c-5*6c^2=0

We add all the numbers together, and all the variables

5c-5*6c^2=0

Wy multiply elements

-30c^2+5c=0

a = -30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-30)·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*-30}=\frac{-10}{-60}
=1/6
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60}
=0
$