F(x)=-2x^2+16x-26

Solution for F(x)=-2x^2+16x-26 equation:

(F)=-2F^2+16F-26

We move all terms to the left:

(F)-(-2F^2+16F-26)=0

We get rid of parentheses

2F^2-16F+F+26=0

We add all the numbers together, and all the variables

2F^2-15F+26=0

a = 2; b = -15; c = +26;
Δ = b2-4ac
Δ = -152-4·2·26
Δ = 17
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{-(-15)-\sqrt{17}}{2*2}=\frac{15-\sqrt{17}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{17}}{2*2}=\frac{15+\sqrt{17}}{4}
$