2c+5=14+21/3c

Solution for 2c+5=14+21/3c equation:

2c+5=14+21/3c

We move all terms to the left:

2c+5-(14+21/3c)=0


Domain of the equation: 3c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

2c-(21/3c+14)+5=0

We get rid of parentheses

2c-21/3c-14+5=0

We multiply all the terms by the denominator


2c*3c-14*3c+5*3c-21=0

Wy multiply elements

6c^2-42c+15c-21=0

We add all the numbers together, and all the variables

6c^2-27c-21=0

a = 6; b = -27; c = -21;
Δ = b2-4ac
Δ = -272-4·6·(-21)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{137}}{2*6}=\frac{27-3\sqrt{137}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{137}}{2*6}=\frac{27+3\sqrt{137}}{12}
$