F(2.5)=2x^2-3x-7

Solution for F(2.5)=2x^2-3x-7 equation:

(2.5)=2F^2-3F-7

We move all terms to the left:

(2.5)-(2F^2-3F-7)=0

We add all the numbers together, and all the variables

-(2F^2-3F-7)+2.5=0

We get rid of parentheses

-2F^2+3F+7+2.5=0

We add all the numbers together, and all the variables

-2F^2+3F+9.5=0

a = -2; b = 3; c = +9.5;
Δ = b2-4ac
Δ = 32-4·(-2)·9.5
Δ = 85
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{-(3)-\sqrt{85}}{2*-2}=\frac{-3-\sqrt{85}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{85}}{2*-2}=\frac{-3+\sqrt{85}}{-4}
$