3/4c+3=-5+c

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

3/4c+3=-5+c

We move all terms to the left:

3/4c+3-(-5+c)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We add all the numbers together, and all the variables

3/4c-(c-5)+3=0

We get rid of parentheses

3/4c-c+5+3=0

We multiply all the terms by the denominator


-c*4c+5*4c+3*4c+3=0

Wy multiply elements

-4c^2+20c+12c+3=0

We add all the numbers together, and all the variables

-4c^2+32c+3=0

a = -4; b = 32; c = +3;
Δ = b2-4ac
Δ = 322-4·(-4)·3
Δ = 1072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{67}}{2*-4}=\frac{-32-4\sqrt{67}}{-8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{67}}{2*-4}=\frac{-32+4\sqrt{67}}{-8}
$