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

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

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

We move all terms to the left:

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


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R



Domain of the equation: 3c-12)!=0

c∈R


We get rid of parentheses

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

We calculate fractions


24c/15c^2+(-10c)/15c^2+12-2=0

We add all the numbers together, and all the variables

24c/15c^2+(-10c)/15c^2+10=0

We multiply all the terms by the denominator


24c+(-10c)+10*15c^2=0

Wy multiply elements

150c^2+24c+(-10c)=0

We get rid of parentheses

150c^2+24c-10c=0

We add all the numbers together, and all the variables

150c^2+14c=0

a = 150; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·150·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*150}=\frac{-28}{300}
=-7/75
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*150}=\frac{0}{300}
=0
$