F(x)=4x^2+5x^2-2

Solution for F(x)=4x^2+5x^2-2 equation:

(F)=4F^2+5F^2-2

We move all terms to the left:

(F)-(4F^2+5F^2-2)=0

We get rid of parentheses

-4F^2-5F^2+F+2=0

We add all the numbers together, and all the variables

-9F^2+F+2=0

a = -9; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-9)·2
Δ = 73
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{73}}{2*-9}=\frac{-1-\sqrt{73}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*-9}=\frac{-1+\sqrt{73}}{-18}
$