F(x)=10x^2+20x-11

Solution for F(x)=10x^2+20x-11 equation:

(F)=10F^2+20F-11

We move all terms to the left:

(F)-(10F^2+20F-11)=0

We get rid of parentheses

-10F^2+F-20F+11=0

We add all the numbers together, and all the variables

-10F^2-19F+11=0

a = -10; b = -19; c = +11;
Δ = b2-4ac
Δ = -192-4·(-10)·11
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{89}}{2*-10}=\frac{19-3\sqrt{89}}{-20}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{89}}{2*-10}=\frac{19+3\sqrt{89}}{-20}
$