F(x)=-3x2+75

Solution for F(x)=-3x2+75 equation:

(F)=-3F^2+75

We move all terms to the left:

(F)-(-3F^2+75)=0

We get rid of parentheses

3F^2+F-75=0

a = 3; b = 1; c = -75;
Δ = b2-4ac
Δ = 12-4·3·(-75)
Δ = 901
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{901}}{2*3}=\frac{-1-\sqrt{901}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{901}}{2*3}=\frac{-1+\sqrt{901}}{6}
$