P(2)=2x^2+100-800

Solution for P(2)=2x^2+100-800 equation:

(2)=2P^2+100-800

We move all terms to the left:

(2)-(2P^2+100-800)=0

We get rid of parentheses

-2P^2-100+800+2=0

We add all the numbers together, and all the variables

-2P^2+702=0

a = -2; b = 0; c = +702;
Δ = b2-4ac
Δ = 02-4·(-2)·702
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{39}}{2*-2}=\frac{0-12\sqrt{39}}{-4}
=-\frac{12\sqrt{39}}{-4}
=-\frac{3\sqrt{39}}{-1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{39}}{2*-2}=\frac{0+12\sqrt{39}}{-4}
=\frac{12\sqrt{39}}{-4}
=\frac{3\sqrt{39}}{-1}
$