1/4c+3=-2c+21

Solution for 1/4c+3=-2c+21 equation:

1/4c+3=-2c+21

We move all terms to the left:

1/4c+3-(-2c+21)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We get rid of parentheses

1/4c+2c-21+3=0

We multiply all the terms by the denominator


2c*4c-21*4c+3*4c+1=0

Wy multiply elements

8c^2-84c+12c+1=0

We add all the numbers together, and all the variables

8c^2-72c+1=0

a = 8; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·8·1
Δ = 5152
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:

$\sqrt{\Delta}=\sqrt{5152}=\sqrt{16*322}=\sqrt{16}*\sqrt{322}=4\sqrt{322}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{322}}{2*8}=\frac{72-4\sqrt{322}}{16}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{322}}{2*8}=\frac{72+4\sqrt{322}}{16}
$