F(x)=2x^2-9x^2+5

Solution for F(x)=2x^2-9x^2+5 equation:

(F)=2F^2-9F^2+5

We move all terms to the left:

(F)-(2F^2-9F^2+5)=0

We get rid of parentheses

-2F^2+9F^2+F-5=0

We add all the numbers together, and all the variables

7F^2+F-5=0

a = 7; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·7·(-5)
Δ = 141
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{141}}{2*7}=\frac{-1-\sqrt{141}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*7}=\frac{-1+\sqrt{141}}{14}
$