F(x)=2x^2-20x-17

Solution for F(x)=2x^2-20x-17 equation:

(F)=2F^2-20F-17

We move all terms to the left:

(F)-(2F^2-20F-17)=0

We get rid of parentheses

-2F^2+F+20F+17=0

We add all the numbers together, and all the variables

-2F^2+21F+17=0

a = -2; b = 21; c = +17;
Δ = b2-4ac
Δ = 212-4·(-2)·17
Δ = 577
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{-(21)-\sqrt{577}}{2*-2}=\frac{-21-\sqrt{577}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{577}}{2*-2}=\frac{-21+\sqrt{577}}{-4}
$