F(10)=3x^2-5x+3

Solution for F(10)=3x^2-5x+3 equation:

(10)=3F^2-5F+3

We move all terms to the left:

(10)-(3F^2-5F+3)=0

We get rid of parentheses

-3F^2+5F-3+10=0

We add all the numbers together, and all the variables

-3F^2+5F+7=0

a = -3; b = 5; c = +7;
Δ = b2-4ac
Δ = 52-4·(-3)·7
Δ = 109
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{-(5)-\sqrt{109}}{2*-3}=\frac{-5-\sqrt{109}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{109}}{2*-3}=\frac{-5+\sqrt{109}}{-6}
$