9/c+12=4c

Solution for 9/c+12=4c equation:

9/c+12=4c

We move all terms to the left:

9/c+12-(4c)=0


Domain of the equation: c!=0

c∈R


We add all the numbers together, and all the variables

-4c+9/c+12=0

We multiply all the terms by the denominator


-4c*c+12*c+9=0

We add all the numbers together, and all the variables

12c-4c*c+9=0

Wy multiply elements

-4c^2+12c+9=0

a = -4; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-4)·9
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*-4}=\frac{-12-12\sqrt{2}}{-8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*-4}=\frac{-12+12\sqrt{2}}{-8}
$