F(x)=X^2+48x-100

Solution for F(x)=X^2+48x-100 equation:

(F)=F^2+48F-100

We move all terms to the left:

(F)-(F^2+48F-100)=0

We get rid of parentheses

-F^2+F-48F+100=0

We add all the numbers together, and all the variables

-1F^2-47F+100=0

a = -1; b = -47; c = +100;
Δ = b2-4ac
Δ = -472-4·(-1)·100
Δ = 2609
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{-(-47)-\sqrt{2609}}{2*-1}=\frac{47-\sqrt{2609}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2609}}{2*-1}=\frac{47+\sqrt{2609}}{-2}
$