F(x)=12x^2+6x-5

Solution for F(x)=12x^2+6x-5 equation:

(F)=12F^2+6F-5

We move all terms to the left:

(F)-(12F^2+6F-5)=0

We get rid of parentheses

-12F^2+F-6F+5=0

We add all the numbers together, and all the variables

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

a = -12; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-12)·5
Δ = 265
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{-(-5)-\sqrt{265}}{2*-12}=\frac{5-\sqrt{265}}{-24}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{265}}{2*-12}=\frac{5+\sqrt{265}}{-24}
$