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

Solution for F(x)=5x^2+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 = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{31}}{2*-5}=\frac{8-2\sqrt{31}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{31}}{2*-5}=\frac{8+2\sqrt{31}}{-10}
$