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

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

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

We move all terms to the left:

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

a = -5; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-5)·6
Δ = 145
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{145}}{2*-5}=\frac{-5-\sqrt{145}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*-5}=\frac{-5+\sqrt{145}}{-10}
$