3/8c-1/5c=7

Solution for 3/8c-1/5c=7 equation:

3/8c-1/5c=7

We move all terms to the left:

3/8c-1/5c-(7)=0


Domain of the equation: 8c!=0

c!=0/8

c!=0

c∈R



Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We calculate fractions


15c/40c^2+(-8c)/40c^2-7=0

We multiply all the terms by the denominator


15c+(-8c)-7*40c^2=0

Wy multiply elements

-280c^2+15c+(-8c)=0

We get rid of parentheses

-280c^2+15c-8c=0

We add all the numbers together, and all the variables

-280c^2+7c=0

a = -280; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-280)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-280}=\frac{-14}{-560}
=1/40
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-280}=\frac{0}{-560}
=0
$