F(x)=5x2-10x+6

Solution for F(x)=5x2-10x+6 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5F^2+11F-6=0

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