6/5c+-6=c+7

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

6/5c+-6=c+7

We move all terms to the left:

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


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6/5c-c-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -5; b = -35; c = +6;
Δ = b2-4ac
Δ = -352-4·(-5)·6
Δ = 1345
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{-(-35)-\sqrt{1345}}{2*-5}=\frac{35-\sqrt{1345}}{-10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1345}}{2*-5}=\frac{35+\sqrt{1345}}{-10}
$