F(x)=-3x^2-6x+5

Solution for F(x)=-3x^2-6x+5 equation:

(F)=-3F^2-6F+5

We move all terms to the left:

(F)-(-3F^2-6F+5)=0

We get rid of parentheses

3F^2+6F+F-5=0

We add all the numbers together, and all the variables

3F^2+7F-5=0

a = 3; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·3·(-5)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{109}}{2*3}=\frac{-7-\sqrt{109}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*3}=\frac{-7+\sqrt{109}}{6}
$