2/3c-13=17,c

Solution for 2/3c-13=17,c equation:

2/3c-13=17.c

We move all terms to the left:

2/3c-13-(17.c)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We add all the numbers together, and all the variables

2/3c-(+17.c)-13=0

We get rid of parentheses

2/3c-17.c-13=0

We multiply all the terms by the denominator


-(17.c)*3c-13*3c+2=0

We add all the numbers together, and all the variables

-(+17.c)*3c-13*3c+2=0

We multiply parentheses

-51c^2-13*3c+2=0

Wy multiply elements

-51c^2-39c+2=0

a = -51; b = -39; c = +2;
Δ = b2-4ac
Δ = -392-4·(-51)·2
Δ = 1929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1929}}{2*-51}=\frac{39-\sqrt{1929}}{-102}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1929}}{2*-51}=\frac{39+\sqrt{1929}}{-102}
$