F(x)=5x2+9x+3

Solution for F(x)=5x2+9x+3 equation:

(F)=5F^2+9F+3

We move all terms to the left:

(F)-(5F^2+9F+3)=0

We get rid of parentheses

-5F^2+F-9F-3=0

We add all the numbers together, and all the variables

-5F^2-8F-3=0

a = -5; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·(-5)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*-5}=\frac{6}{-10}
=-3/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*-5}=\frac{10}{-10}
=-1
$