1/5c+3/4c=11

Solution for 1/5c+3/4c=11 equation:

1/5c+3/4c=11

We move all terms to the left:

1/5c+3/4c-(11)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R



Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We calculate fractions


4c/20c^2+15c/20c^2-11=0

We multiply all the terms by the denominator


4c+15c-11*20c^2=0

We add all the numbers together, and all the variables

19c-11*20c^2=0

Wy multiply elements

-220c^2+19c=0

a = -220; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-220)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-220}=\frac{-38}{-440}
=19/220
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-220}=\frac{0}{-440}
=0
$