2/5c+4/5c+2=c+7

Solution for 2/5c+4/5c+2=c+7 equation:

2/5c+4/5c+2=c+7

We move all terms to the left:

2/5c+4/5c+2-(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+2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-5c^2-35c+10c+6=0

We add all the numbers together, and all the variables

-5c^2-25c+6=0

a = -5; b = -25; c = +6;
Δ = b2-4ac
Δ = -252-4·(-5)·6
Δ = 745
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{-(-25)-\sqrt{745}}{2*-5}=\frac{25-\sqrt{745}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{745}}{2*-5}=\frac{25+\sqrt{745}}{-10}
$