F(x)=6x^2+13x-5

Solution for F(x)=6x^2+13x-5 equation:

(F)=6F^2+13F-5

We move all terms to the left:

(F)-(6F^2+13F-5)=0

We get rid of parentheses

-6F^2+F-13F+5=0

We add all the numbers together, and all the variables

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

a = -6; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·(-6)·5
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*-6}=\frac{12-2\sqrt{66}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*-6}=\frac{12+2\sqrt{66}}{-12}
$