F(x)=x^2-11x+10

Solution for F(x)=x^2-11x+10 equation:

(F)=F^2-11F+10

We move all terms to the left:

(F)-(F^2-11F+10)=0

We get rid of parentheses

-F^2+F+11F-10=0

We add all the numbers together, and all the variables

-1F^2+12F-10=0

a = -1; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·(-1)·(-10)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*-1}=\frac{-12-2\sqrt{26}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*-1}=\frac{-12+2\sqrt{26}}{-2}
$