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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+3F+12=0

a = -2; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-2)·12
Δ = 105
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{-(3)-\sqrt{105}}{2*-2}=\frac{-3-\sqrt{105}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-2}=\frac{-3+\sqrt{105}}{-4}
$