F(x)=3x^2+6x-11

Solution for F(x)=3x^2+6x-11 equation:

(F)=3F^2+6F-11

We move all terms to the left:

(F)-(3F^2+6F-11)=0

We get rid of parentheses

-3F^2+F-6F+11=0

We add all the numbers together, and all the variables

-3F^2-5F+11=0

a = -3; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-3)·11
Δ = 157
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{157}}{2*-3}=\frac{5-\sqrt{157}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{157}}{2*-3}=\frac{5+\sqrt{157}}{-6}
$