F(2)=2x^2-7x-15

Solution for F(2)=2x^2-7x-15 equation:

(2)=2F^2-7F-15

We move all terms to the left:

(2)-(2F^2-7F-15)=0

We get rid of parentheses

-2F^2+7F+15+2=0

We add all the numbers together, and all the variables

-2F^2+7F+17=0

a = -2; b = 7; c = +17;
Δ = b2-4ac
Δ = 72-4·(-2)·17
Δ = 185
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{-(7)-\sqrt{185}}{2*-2}=\frac{-7-\sqrt{185}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{185}}{2*-2}=\frac{-7+\sqrt{185}}{-4}
$