C(x)=900/x+30

Solution for C(x)=900/x+30 equation:

(C)=900/C+30

We move all terms to the left:

(C)-(900/C+30)=0


Domain of the equation: C+30)!=0

C∈R


We get rid of parentheses

C-900/C-30=0

We multiply all the terms by the denominator


C*C-30*C-900=0

We add all the numbers together, and all the variables

-30C+C*C-900=0

Wy multiply elements

C^2-30C-900=0

a = 1; b = -30; c = -900;
Δ = b2-4ac
Δ = -302-4·1·(-900)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{5}}{2*1}=\frac{30-30\sqrt{5}}{2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{5}}{2*1}=\frac{30+30\sqrt{5}}{2}
$