F(x)=x2+2x-48

Solution for F(x)=x2+2x-48 equation:

(F)=F2+2F-48

We move all terms to the left:

(F)-(F2+2F-48)=0

We add all the numbers together, and all the variables

-(+F^2+2F-48)+F=0

We get rid of parentheses

-F^2-2F+F+48=0

We add all the numbers together, and all the variables

-1F^2-1F+48=0

a = -1; b = -1; c = +48;
Δ = b2-4ac
Δ = -12-4·(-1)·48
Δ = 193
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{193}}{2*-1}=\frac{1-\sqrt{193}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{193}}{2*-1}=\frac{1+\sqrt{193}}{-2}
$