2/c+5=5c+10

Solution for 2/c+5=5c+10 equation:

2/c+5=5c+10

We move all terms to the left:

2/c+5-(5c+10)=0


Domain of the equation: c!=0

c∈R


We get rid of parentheses

2/c-5c-10+5=0

We multiply all the terms by the denominator


-5c*c-10*c+5*c+2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-5c^2-5c+2=0

a = -5; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-5)·2
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{65}}{2*-5}=\frac{5-\sqrt{65}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-5}=\frac{5+\sqrt{65}}{-10}
$