F(x)=2*x^2-45

Solution for F(x)=2*x^2-45 equation:

(F)=2F^2-45

We move all terms to the left:

(F)-(2F^2-45)=0

We get rid of parentheses

-2F^2+F+45=0

a = -2; b = 1; c = +45;
Δ = b2-4ac
Δ = 12-4·(-2)·45
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*-2}=\frac{-20}{-4}
=+5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*-2}=\frac{18}{-4}
=-4+1/2
$