F(x)=x2+10x+6

Solution for F(x)=x2+10x+6 equation:

(F)=F2+10F+6

We move all terms to the left:

(F)-(F2+10F+6)=0

We add all the numbers together, and all the variables

-(+F^2+10F+6)+F=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2-9F-6=0

a = -1; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·(-1)·(-6)
Δ = 57
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{-(-9)-\sqrt{57}}{2*-1}=\frac{9-\sqrt{57}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*-1}=\frac{9+\sqrt{57}}{-2}
$