F(x)=5x^2-200

Solution for F(x)=5x^2-200 equation:

(F)=5F^2-200

We move all terms to the left:

(F)-(5F^2-200)=0

We get rid of parentheses

-5F^2+F+200=0

a = -5; b = 1; c = +200;
Δ = b2-4ac
Δ = 12-4·(-5)·200
Δ = 4001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{4001}}{2*-5}=\frac{-1-\sqrt{4001}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4001}}{2*-5}=\frac{-1+\sqrt{4001}}{-10}
$