1/3c-2=5c-30

Solution for 1/3c-2=5c-30 equation:

1/3c-2=5c-30

We move all terms to the left:

1/3c-2-(5c-30)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We get rid of parentheses

1/3c-5c+30-2=0

We multiply all the terms by the denominator


-5c*3c+30*3c-2*3c+1=0

Wy multiply elements

-15c^2+90c-6c+1=0

We add all the numbers together, and all the variables

-15c^2+84c+1=0

a = -15; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-15)·1
Δ = 7116
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:

$\sqrt{\Delta}=\sqrt{7116}=\sqrt{4*1779}=\sqrt{4}*\sqrt{1779}=2\sqrt{1779}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1779}}{2*-15}=\frac{-84-2\sqrt{1779}}{-30}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1779}}{2*-15}=\frac{-84+2\sqrt{1779}}{-30}
$