F(3)=x2+5x-7

Solution for F(3)=x2+5x-7 equation:

(3)=F2+5F-7

We move all terms to the left:

(3)-(F2+5F-7)=0

We add all the numbers together, and all the variables

-(+F^2+5F-7)+3=0

We get rid of parentheses

-F^2-5F+7+3=0

We add all the numbers together, and all the variables

-1F^2-5F+10=0

a = -1; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-1)·10
Δ = 65
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{-(-5)-\sqrt{65}}{2*-1}=\frac{5-\sqrt{65}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-1}=\frac{5+\sqrt{65}}{-2}
$