F(x)=2x2+5x-17

Solution for F(x)=2x2+5x-17 equation:

(F)=2F^2+5F-17

We move all terms to the left:

(F)-(2F^2+5F-17)=0

We get rid of parentheses

-2F^2+F-5F+17=0

We add all the numbers together, and all the variables

-2F^2-4F+17=0

a = -2; b = -4; c = +17;
Δ = b2-4ac
Δ = -42-4·(-2)·17
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{38}}{2*-2}=\frac{4-2\sqrt{38}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{38}}{2*-2}=\frac{4+2\sqrt{38}}{-4}
$