F(x)=2x^2-12x-23

Solution for F(x)=2x^2-12x-23 equation:

(F)=2F^2-12F-23

We move all terms to the left:

(F)-(2F^2-12F-23)=0

We get rid of parentheses

-2F^2+F+12F+23=0

We add all the numbers together, and all the variables

-2F^2+13F+23=0

a = -2; b = 13; c = +23;
Δ = b2-4ac
Δ = 132-4·(-2)·23
Δ = 353
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{-(13)-\sqrt{353}}{2*-2}=\frac{-13-\sqrt{353}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{353}}{2*-2}=\frac{-13+\sqrt{353}}{-4}
$