C(x)=1/4x+-3

Solution for C(x)=1/4x+-3 equation:

(C)=1/4C+-3

We move all terms to the left:

(C)-(1/4C+-3)=0


Domain of the equation: 4C+-3)!=0

C∈R


We add all the numbers together, and all the variables

C-(1/4C-3)=0

We get rid of parentheses

C-1/4C+3=0

We multiply all the terms by the denominator


C*4C+3*4C-1=0

Wy multiply elements

4C^2+12C-1=0

a = 4; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*4}=\frac{-12-4\sqrt{10}}{8}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*4}=\frac{-12+4\sqrt{10}}{8}
$