C(x)=0.2x(0.2x)-36x+18,689

Solution for C(x)=0.2x(0.2x)-36x+18,689 equation:

(C)=0.2C(0.2C)-36C+18.689

We move all terms to the left:

(C)-(0.2C(0.2C)-36C+18.689)=0

We add all the numbers together, and all the variables

C-(0.2C(+0.2C)-36C+18.689)=0


We calculate terms in parentheses: -(0.2C(+0.2C)-36C+18.689), so:

0.2C(+0.2C)-36C+18.689

We add all the numbers together, and all the variables

-36C+0.2C(+0.2C)+18.689

We multiply parentheses

0C^2-36C+18.689

We add all the numbers together, and all the variables

C^2-36C+18.689

Back to the equation:

-(C^2-36C+18.689)


We get rid of parentheses

-C^2+C+36C-18.689=0

We add all the numbers together, and all the variables

-1C^2+37C-18.689=0

a = -1; b = 37; c = -18.689;
Δ = b2-4ac
Δ = 372-4·(-1)·(-18.689)
Δ = 1294.244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-\sqrt{1294.244}}{2*-1}=\frac{-37-\sqrt{1294.244}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{1294.244}}{2*-1}=\frac{-37+\sqrt{1294.244}}{-2}
$