F(x)=12x^2-25x-7

Solution for F(x)=12x^2-25x-7 equation:

(F)=12F^2-25F-7

We move all terms to the left:

(F)-(12F^2-25F-7)=0

We get rid of parentheses

-12F^2+F+25F+7=0

We add all the numbers together, and all the variables

-12F^2+26F+7=0

a = -12; b = 26; c = +7;
Δ = b2-4ac
Δ = 262-4·(-12)·7
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{253}}{2*-12}=\frac{-26-2\sqrt{253}}{-24}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{253}}{2*-12}=\frac{-26+2\sqrt{253}}{-24}
$