F(x)=x2+2x+-7

Solution for F(x)=x2+2x+-7 equation:

(F)=F2+2F+-7

We move all terms to the left:

(F)-(F2+2F+-7)=0

We add all the numbers together, and all the variables

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

We use the square of the difference formula

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-1)·7
Δ = 29
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{-(-1)-\sqrt{29}}{2*-1}=\frac{1-\sqrt{29}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29}}{2*-1}=\frac{1+\sqrt{29}}{-2}
$