5c-2/c=-6

Solution for 5c-2/c=-6 equation:

5c-2/c=-6

We move all terms to the left:

5c-2/c-(-6)=0


Domain of the equation: c!=0

c∈R


We add all the numbers together, and all the variables

5c-2/c+6=0

We multiply all the terms by the denominator


5c*c+6*c-2=0

We add all the numbers together, and all the variables

6c+5c*c-2=0

Wy multiply elements

5c^2+6c-2=0

a = 5; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·5·(-2)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{19}}{2*5}=\frac{-6-2\sqrt{19}}{10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{19}}{2*5}=\frac{-6+2\sqrt{19}}{10}
$