3/4c-51/2c=1

Solution for 3/4c-51/2c=1 equation:

3/4c-51/2c=1

We move all terms to the left:

3/4c-51/2c-(1)=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 calculate fractions


6c/8c^2+(-204c)/8c^2-1=0

We multiply all the terms by the denominator


6c+(-204c)-1*8c^2=0

Wy multiply elements

-8c^2+6c+(-204c)=0

We get rid of parentheses

-8c^2+6c-204c=0

We add all the numbers together, and all the variables

-8c^2-198c=0

a = -8; b = -198; c = 0;
Δ = b2-4ac
Δ = -1982-4·(-8)·0
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-198}{2*-8}=\frac{0}{-16}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+198}{2*-8}=\frac{396}{-16}
=-24+3/4
$