F(x)=10x^2-x-2

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

(F)=10F^2-F-2

We move all terms to the left:

(F)-(10F^2-F-2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -10; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-10)·2
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*-10}=\frac{-2-2\sqrt{21}}{-20}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*-10}=\frac{-2+2\sqrt{21}}{-20}
$