F(x)=6x^2+13x-9

Solution for F(x)=6x^2+13x-9 equation:

(F)=6F^2+13F-9

We move all terms to the left:

(F)-(6F^2+13F-9)=0

We get rid of parentheses

-6F^2+F-13F+9=0

We add all the numbers together, and all the variables

-6F^2-12F+9=0

a = -6; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·(-6)·9
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{10}}{2*-6}=\frac{12-6\sqrt{10}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{10}}{2*-6}=\frac{12+6\sqrt{10}}{-12}
$