1/4c+2/5c=13/2

Solution for 1/4c+2/5c=13/2 equation:

1/4c+2/5c=13/2

We move all terms to the left:

1/4c+2/5c-(13/2)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

1/4c+2/5c-(+13/2)=0

We get rid of parentheses

1/4c+2/5c-13/2=0

We calculate fractions


(-1300c^2)/80c^2+20c/80c^2+32c/80c^2=0

We multiply all the terms by the denominator


(-1300c^2)+20c+32c=0

We add all the numbers together, and all the variables

(-1300c^2)+52c=0

We get rid of parentheses

-1300c^2+52c=0

a = -1300; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-1300)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-1300}=\frac{-104}{-2600}
=1/25
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-1300}=\frac{0}{-2600}
=0
$