2c+c+3/4c=60

Solution for 2c+c+3/4c=60 equation:

2c+c+3/4c=60

We move all terms to the left:

2c+c+3/4c-(60)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We add all the numbers together, and all the variables

3c+3/4c-60=0

We multiply all the terms by the denominator


3c*4c-60*4c+3=0

Wy multiply elements

12c^2-240c+3=0

a = 12; b = -240; c = +3;
Δ = b2-4ac
Δ = -2402-4·12·3
Δ = 57456
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:

$\sqrt{\Delta}=\sqrt{57456}=\sqrt{144*399}=\sqrt{144}*\sqrt{399}=12\sqrt{399}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-12\sqrt{399}}{2*12}=\frac{240-12\sqrt{399}}{24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+12\sqrt{399}}{2*12}=\frac{240+12\sqrt{399}}{24}
$