F(-6)=12-10x-5x^2

Solution for F(-6)=12-10x-5x^2 equation:

(-6)=12-10F-5F^2

We move all terms to the left:

(-6)-(12-10F-5F^2)=0

We add all the numbers together, and all the variables

-(12-10F-5F^2)-6=0

We get rid of parentheses

5F^2+10F-12-6=0

We add all the numbers together, and all the variables

5F^2+10F-18=0

a = 5; b = 10; c = -18;
Δ = b2-4ac
Δ = 102-4·5·(-18)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{115}}{2*5}=\frac{-10-2\sqrt{115}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{115}}{2*5}=\frac{-10+2\sqrt{115}}{10}
$