8/3c-2=23c-12

Solution for 8/3c-2=23c-12 equation:

8/3c-2=23c-12

We move all terms to the left:

8/3c-2-(23c-12)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We get rid of parentheses

8/3c-23c+12-2=0

We multiply all the terms by the denominator


-23c*3c+12*3c-2*3c+8=0

Wy multiply elements

-69c^2+36c-6c+8=0

We add all the numbers together, and all the variables

-69c^2+30c+8=0

a = -69; b = 30; c = +8;
Δ = b2-4ac
Δ = 302-4·(-69)·8
Δ = 3108
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:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{777}}{2*-69}=\frac{-30-2\sqrt{777}}{-138}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{777}}{2*-69}=\frac{-30+2\sqrt{777}}{-138}
$