F(x)=-2x^2+12x-15

Solution for F(x)=-2x^2+12x-15 equation:

(F)=-2F^2+12F-15

We move all terms to the left:

(F)-(-2F^2+12F-15)=0

We get rid of parentheses

2F^2-12F+F+15=0

We add all the numbers together, and all the variables

2F^2-11F+15=0

a = 2; b = -11; c = +15;
Δ = b2-4ac
Δ = -112-4·2·15
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*2}=\frac{10}{4}
=2+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*2}=\frac{12}{4}
=3
$