F(x)=x+x^2-132

Solution for F(x)=x+x^2-132 equation:

(F)=F+F^2-132

We move all terms to the left:

(F)-(F+F^2-132)=0

We get rid of parentheses

-F^2-F+F+132=0

We add all the numbers together, and all the variables

-1F^2+132=0

a = -1; b = 0; c = +132;
Δ = b2-4ac
Δ = 02-4·(-1)·132
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*-1}=\frac{0-4\sqrt{33}}{-2}
=-\frac{4\sqrt{33}}{-2}
=-\frac{2\sqrt{33}}{-1}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*-1}=\frac{0+4\sqrt{33}}{-2}
=\frac{4\sqrt{33}}{-2}
=\frac{2\sqrt{33}}{-1}
$