8/3c-2=2/5c-12

Solution for 8/3c-2=2/5c-12 equation:

8/3c-2=2/5c-12

We move all terms to the left:

8/3c-2-(2/5c-12)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R



Domain of the equation: 5c-12)!=0

c∈R


We get rid of parentheses

8/3c-2/5c+12-2=0

We calculate fractions


40c/15c^2+(-6c)/15c^2+12-2=0

We add all the numbers together, and all the variables

40c/15c^2+(-6c)/15c^2+10=0

We multiply all the terms by the denominator


40c+(-6c)+10*15c^2=0

Wy multiply elements

150c^2+40c+(-6c)=0

We get rid of parentheses

150c^2+40c-6c=0

We add all the numbers together, and all the variables

150c^2+34c=0

a = 150; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·150·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*150}=\frac{-68}{300}
=-17/75
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*150}=\frac{0}{300}
=0
$