F(x)=x2-6.5

Solution for F(x)=x2-6.5 equation:

(F)=F2-6.5

We move all terms to the left:

(F)-(F2-6.5)=0

We add all the numbers together, and all the variables

-(+F^2-6.5)+F=0

We get rid of parentheses

-F^2+F+6.5=0

We add all the numbers together, and all the variables

-1F^2+F+6.5=0

a = -1; b = 1; c = +6.5;
Δ = b2-4ac
Δ = 12-4·(-1)·6.5
Δ = 27
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:

$\sqrt{\Delta}=\sqrt{27}=\sqrt{9*3}=\sqrt{9}*\sqrt{3}=3\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{3}}{2*-1}=\frac{-1-3\sqrt{3}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{3}}{2*-1}=\frac{-1+3\sqrt{3}}{-2}
$