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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-4)·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-4}=\frac{-4}{-8}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-4}=\frac{12}{-8}
=-1+1/2
$