3/4c-1/3c=10

Solution for 3/4c-1/3c=10 equation:

3/4c-1/3c=10

We move all terms to the left:

3/4c-1/3c-(10)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We calculate fractions


9c/12c^2+(-4c)/12c^2-10=0

We multiply all the terms by the denominator


9c+(-4c)-10*12c^2=0

Wy multiply elements

-120c^2+9c+(-4c)=0

We get rid of parentheses

-120c^2+9c-4c=0

We add all the numbers together, and all the variables

-120c^2+5c=0

a = -120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-120)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-120}=\frac{-10}{-240}
=1/24
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240}
=0
$