C=1200-30x+0.14x^2

Solution for C=1200-30x+0.14x^2 equation:

=1200-30C+0.14C^2

We move all terms to the left:

-(1200-30C+0.14C^2)=0

We get rid of parentheses

-0.14C^2+30C-1200=0

a = -0.14; b = 30; c = -1200;
Δ = b2-4ac
Δ = 302-4·(-0.14)·(-1200)
Δ = 228
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{-(30)-\sqrt{228}}{2*-0.14}=\frac{-30-\sqrt{228}}{-0.28}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{228}}{2*-0.14}=\frac{-30+\sqrt{228}}{-0.28}
$