1/(c-6)=-5/2c+9

Solution for 1/(c-6)=-5/2c+9 equation:

1/(c-6)=-5/2c+9

We move all terms to the left:

1/(c-6)-(-5/2c+9)=0


Domain of the equation: (c-6)!=0

We move all terms containing c to the left, all other terms to the right

c!=6

c∈R



Domain of the equation: 2c+9)!=0

c∈R


We get rid of parentheses

1/(c-6)+5/2c-9=0

We calculate fractions


2c/(2c^2-12c)+(5c-30)/(2c^2-12c)-9=0

We multiply all the terms by the denominator


2c+(5c-30)-9*(2c^2-12c)=0

We multiply parentheses

-18c^2+2c+(5c-30)+108c=0

We get rid of parentheses

-18c^2+2c+5c+108c-30=0

We add all the numbers together, and all the variables

-18c^2+115c-30=0

a = -18; b = 115; c = -30;
Δ = b2-4ac
Δ = 1152-4·(-18)·(-30)
Δ = 11065
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{-(115)-\sqrt{11065}}{2*-18}=\frac{-115-\sqrt{11065}}{-36}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+\sqrt{11065}}{2*-18}=\frac{-115+\sqrt{11065}}{-36}
$