3/4c+1/2=5/6c-2

Solution for 3/4c+1/2=5/6c-2 equation:

3/4c+1/2=5/6c-2

We move all terms to the left:

3/4c+1/2-(5/6c-2)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R



Domain of the equation: 6c-2)!=0

c∈R


We get rid of parentheses

3/4c-5/6c+2+1/2=0

We calculate fractions


144c^2/96c^2+72c/96c^2+(-80c)/96c^2+2=0

We multiply all the terms by the denominator


144c^2+72c+(-80c)+2*96c^2=0

Wy multiply elements

144c^2+192c^2+72c+(-80c)=0

We get rid of parentheses

144c^2+192c^2+72c-80c=0

We add all the numbers together, and all the variables

336c^2-8c=0

a = 336; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·336·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*336}=\frac{0}{672}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*336}=\frac{16}{672}
=1/42
$