F(x)=2x^2-6x-1

Solution for F(x)=2x^2-6x-1 equation:

(F)=2F^2-6F-1

We move all terms to the left:

(F)-(2F^2-6F-1)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+7F+1=0

a = -2; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-2)·1
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{-(7)-\sqrt{57}}{2*-2}=\frac{-7-\sqrt{57}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{57}}{2*-2}=\frac{-7+\sqrt{57}}{-4}
$