F(x)=x^2-10x+30

Solution for F(x)=x^2-10x+30 equation:

(F)=F^2-10F+30

We move all terms to the left:

(F)-(F^2-10F+30)=0

We get rid of parentheses

-F^2+F+10F-30=0

We add all the numbers together, and all the variables

-1F^2+11F-30=0

a = -1; b = 11; c = -30;
Δ = b2-4ac
Δ = 112-4·(-1)·(-30)
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*-1}=\frac{-12}{-2}
=+6
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*-1}=\frac{-10}{-2}
=+5
$