8.3c-2=2/3c-12

Solution for 8.3c-2=2/3c-12 equation:

8.3c-2=2/3c-12

We move all terms to the left:

8.3c-2-(2/3c-12)=0


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

c∈R


We get rid of parentheses

8.3c-2/3c+12-2=0

We multiply all the terms by the denominator


(8.3c)*3c+12*3c-2*3c-2=0

We add all the numbers together, and all the variables

(+8.3c)*3c+12*3c-2*3c-2=0

We multiply parentheses

24c^2+12*3c-2*3c-2=0

Wy multiply elements

24c^2+36c-6c-2=0

We add all the numbers together, and all the variables

24c^2+30c-2=0

a = 24; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·24·(-2)
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{273}}{2*24}=\frac{-30-2\sqrt{273}}{48}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{273}}{2*24}=\frac{-30+2\sqrt{273}}{48}
$