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

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

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

We move all terms to the left:

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


Domain of the equation: c!=0

c∈R



Domain of the equation: 5c-14)!=0

c∈R


We get rid of parentheses

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

We calculate fractions


c-c+(-15c)/5c^2+(-2c)/5c^2+14=0

We add all the numbers together, and all the variables

(-15c)/5c^2+(-2c)/5c^2+14=0

We multiply all the terms by the denominator


(-15c)+(-2c)+14*5c^2=0

Wy multiply elements

70c^2+(-15c)+(-2c)=0

We get rid of parentheses

70c^2-15c-2c=0

We add all the numbers together, and all the variables

70c^2-17c=0

a = 70; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·70·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*70}=\frac{0}{140}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*70}=\frac{34}{140}
=17/70
$