c-3/2c+4=5/2c+7-3

Solution for c-3/2c+4=5/2c+7-3 equation:

c-3/2c+4=5/2c+7-3

We move all terms to the left:

c-3/2c+4-(5/2c+7-3)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R



Domain of the equation: 2c+7-3)!=0

We move all terms containing c to the left, all other terms to the right

2c-3)!=-7

c∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


c*2c-4*2c+4*2c-3-5=0

We add all the numbers together, and all the variables

c*2c-4*2c+4*2c-8=0

Wy multiply elements

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

We add all the numbers together, and all the variables

2c^2-8=0

a = 2; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·2·(-8)
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{-(0)-8}{2*2}=\frac{-8}{4}
=-2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*2}=\frac{8}{4}
=2
$