F(x)=-20x2+23x-6

Solution for F(x)=-20x2+23x-6 equation:

(F)=-20F^2+23F-6

We move all terms to the left:

(F)-(-20F^2+23F-6)=0

We get rid of parentheses

20F^2-23F+F+6=0

We add all the numbers together, and all the variables

20F^2-22F+6=0

a = 20; b = -22; c = +6;
Δ = b2-4ac
Δ = -222-4·20·6
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{-(-22)-2}{2*20}=\frac{20}{40}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2}{2*20}=\frac{24}{40}
=3/5
$