P=980x-20,000+40x^2+x^2

Solution for P=980x-20,000+40x^2+x^2 equation:

=980P-20.000+40P^2+P^2

We move all terms to the left:

-(980P-20.000+40P^2+P^2)=0

We get rid of parentheses

-40P^2-P^2-980P+20.000=0

We add all the numbers together, and all the variables

-41P^2-980P+20=0

a = -41; b = -980; c = +20;
Δ = b2-4ac
Δ = -9802-4·(-41)·20
Δ = 963680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{963680}=\sqrt{16*60230}=\sqrt{16}*\sqrt{60230}=4\sqrt{60230}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-980)-4\sqrt{60230}}{2*-41}=\frac{980-4\sqrt{60230}}{-82}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-980)+4\sqrt{60230}}{2*-41}=\frac{980+4\sqrt{60230}}{-82}
$