(2)/(5)c+(4)/(5)c-6=c+7

Solution for (2)/(5)c+(4)/(5)c-6=c+7 equation:

(2)/(5)c+(4)/(5)c-6=c+7

We move all terms to the left:

(2)/(5)c+(4)/(5)c-6-(c+7)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We get rid of parentheses

2/5c+4/5c-c-7-6=0

We multiply all the terms by the denominator


-c*5c-7*5c-6*5c+2+4=0

We add all the numbers together, and all the variables

-c*5c-7*5c-6*5c+6=0

Wy multiply elements

-5c^2-35c-30c+6=0

We add all the numbers together, and all the variables

-5c^2-65c+6=0

a = -5; b = -65; c = +6;
Δ = b2-4ac
Δ = -652-4·(-5)·6
Δ = 4345
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{-(-65)-\sqrt{4345}}{2*-5}=\frac{65-\sqrt{4345}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4345}}{2*-5}=\frac{65+\sqrt{4345}}{-10}
$