F(x)=2x2-5x-12

Solution for F(x)=2x2-5x-12 equation:

(F)=2F^2-5F-12

We move all terms to the left:

(F)-(2F^2-5F-12)=0

We get rid of parentheses

-2F^2+F+5F+12=0

We add all the numbers together, and all the variables

-2F^2+6F+12=0

a = -2; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-2)·12
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*-2}=\frac{-6-2\sqrt{33}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*-2}=\frac{-6+2\sqrt{33}}{-4}
$