3/4c+1/2c=6/7

Solution for 3/4c+1/2c=6/7 equation:

3/4c+1/2c=6/7

We move all terms to the left:

3/4c+1/2c-(6/7)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

3/4c+1/2c-(+6/7)=0

We get rid of parentheses

3/4c+1/2c-6/7=0

We calculate fractions


(-96c^2)/392c^2+294c/392c^2+196c/392c^2=0

We multiply all the terms by the denominator


(-96c^2)+294c+196c=0

We add all the numbers together, and all the variables

(-96c^2)+490c=0

We get rid of parentheses

-96c^2+490c=0

a = -96; b = 490; c = 0;
Δ = b2-4ac
Δ = 4902-4·(-96)·0
Δ = 240100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{240100}=490$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(490)-490}{2*-96}=\frac{-980}{-192}
=5+5/48
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(490)+490}{2*-96}=\frac{0}{-192}
=0
$