F(5)=-3x+4x^2

Solution for F(5)=-3x+4x^2 equation:

(5)=-3F+4F^2

We move all terms to the left:

(5)-(-3F+4F^2)=0

We get rid of parentheses

-4F^2+3F+5=0

a = -4; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-4)·5
Δ = 89
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{-(3)-\sqrt{89}}{2*-4}=\frac{-3-\sqrt{89}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*-4}=\frac{-3+\sqrt{89}}{-8}
$