1/10c+1/4c=21

Solution for 1/10c+1/4c=21 equation:

1/10c+1/4c=21

We move all terms to the left:

1/10c+1/4c-(21)=0


Domain of the equation: 10c!=0

c!=0/10

c!=0

c∈R



Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We calculate fractions


4c/40c^2+10c/40c^2-21=0

We multiply all the terms by the denominator


4c+10c-21*40c^2=0

We add all the numbers together, and all the variables

14c-21*40c^2=0

Wy multiply elements

-840c^2+14c=0

a = -840; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-840)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-840}=\frac{-28}{-1680}
=1/60
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-840}=\frac{0}{-1680}
=0
$