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

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

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

We move all terms to the left:

3/4c-5-1/2c-(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 add all the numbers together, and all the variables

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

We calculate fractions


6c/8c^2+(-4c)/8c^2-6=0

We multiply all the terms by the denominator


6c+(-4c)-6*8c^2=0

Wy multiply elements

-48c^2+6c+(-4c)=0

We get rid of parentheses

-48c^2+6c-4c=0

We add all the numbers together, and all the variables

-48c^2+2c=0

a = -48; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-48)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-48}=\frac{-4}{-96}
=1/24
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-48}=\frac{0}{-96}
=0
$