F(10)=100x-4x^2

Solution for F(10)=100x-4x^2 equation:

(10)=100F-4F^2

We move all terms to the left:

(10)-(100F-4F^2)=0

We get rid of parentheses

4F^2-100F+10=0

a = 4; b = -100; c = +10;
Δ = b2-4ac
Δ = -1002-4·4·10
Δ = 9840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9840}=\sqrt{16*615}=\sqrt{16}*\sqrt{615}=4\sqrt{615}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{615}}{2*4}=\frac{100-4\sqrt{615}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{615}}{2*4}=\frac{100+4\sqrt{615}}{8}
$