c+1=1/2c+4

Solution for c+1=1/2c+4 equation:

c+1=1/2c+4

We move all terms to the left:

c+1-(1/2c+4)=0


Domain of the equation: 2c+4)!=0

c∈R


We get rid of parentheses

c-1/2c-4+1=0

We multiply all the terms by the denominator


c*2c-4*2c+1*2c-1=0

Wy multiply elements

2c^2-8c+2c-1=0

We add all the numbers together, and all the variables

2c^2-6c-1=0

a = 2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·2·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*2}=\frac{6-2\sqrt{11}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*2}=\frac{6+2\sqrt{11}}{4}
$