1/3c+3/8c=3/4

Solution for 1/3c+3/8c=3/4 equation:

1/3c+3/8c=3/4

We move all terms to the left:

1/3c+3/8c-(3/4)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R



Domain of the equation: 8c!=0

c!=0/8

c!=0

c∈R


We add all the numbers together, and all the variables

1/3c+3/8c-(+3/4)=0

We get rid of parentheses

1/3c+3/8c-3/4=0

We calculate fractions


(-576c^2)/384c^2+128c/384c^2+144c/384c^2=0

We multiply all the terms by the denominator


(-576c^2)+128c+144c=0

We add all the numbers together, and all the variables

(-576c^2)+272c=0

We get rid of parentheses

-576c^2+272c=0

a = -576; b = 272; c = 0;
Δ = b2-4ac
Δ = 2722-4·(-576)·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-272}{2*-576}=\frac{-544}{-1152}
=17/36
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+272}{2*-576}=\frac{0}{-1152}
=0
$